Blocking stairs but mother climbs rail. Any suggestions?

Wow. Goes to prove where there is a will there is a way.
I would have someone place a solid panel along the open area that she might climb. If this is a stairway that is “central” where one side of the stairs does not have a wall next to it you would have to do both sides.
You could get clear so that it is not noticeable but that might be more dangerous as your mom might not see that it is there and still try to climb. I would look at the plastic grid type and they come in white.
Another possibly less expensive option to try would be get a bunch of “pool noodles” the kind with a hole down the center. Cut them down the center and slip a noodle around each of the rungs going up the stairs. The noodles would take up the space that her foot would go so there is less of a chance she could climb.
If this is the only safety issue you can keep trying to figure it out BUT this might be a case where she would be safer in a place with no stairs and have someone available 24/7 to watch her.
My Husband tried all different ways to get out of the house. At one point I had keys to my car in a safe. Switched to wearing them on my belt loop attached to a carabiner, I wore the keys to the house around my neck for 5 years so he could not escape I changed all the locks on the doors to double sided locks and I cable tied my dining room furniture together so he could not take chairs and climb over the porch railing, and I had a lock on the gate I put on the porch. All to keep him from wandering off.
It does not end until they lose the ability to walk. And that brings another set of challenges. It is always something!

My Mom was roaming the house at night. I found her 1 morning on the floor in the kitchen. On another morning, I got up and there was poop every where. Family room, kitchen floor, poop foot prints. It was nasty. I alarmed her bedroom door. I also spoke to her Dr and she placed my Mom on Trazadone to help her sleep at night. My Mom now sleeps thru the night. Maybe 2x a month she will get up. I put her back to bed and she goes back to sleep. No more roaming at night.

I am again dumbfounded what people will allow their spouses or parents or whoever to get away with. I do not know the answer as to how to stop this behavior - perhaps a very strong sleeping pill might help. However, behavior that is so often exhibited by mental patients has such negative effects on the rest of the family and in some cases will destroy the family unit. That is when I draw the line - it cannot be stopped but I do not have to take the abuse and problems. My solution is - hard as it may be - they must be placed. I know this sounds harsh but normal people have a right to live their lives now - before their day arrives.

I'd be very reluctant to use physical barriers to prevent her from the stairs. At this point she has the agility and persistence to climb unsafely to bypass the barrier. The ability of an elder with dementia who is determined to go somewhere can be very very strong! 
You might want to put alarms on your exit doors, so that she can't decide to walk to the market or church or whatever......even if it hasn't happened yet.....
Some type of motion activated alarm that could be placed at the foot of the stairs or on a door frame that is on her pathway to the stairs would let you know she was on the move. It might startle her and get her to turn around and go back to her room...or not.
Getting outside and going for a walk at the park or even a long scenic ride can help improve sleep. Sunshine is good for the brain.
Trazodone at bedtime helps a lot. Well tolerated by elders. Also, a couple of acetaminophen tablets in the evening or at bedtime help relieve the discomfort of aches and pains that are not bothersome or even noticed in the daytime, but can be more bothersome in the dark. Elders do not have as much deep sleep as they did, and so stiffness and soreness can interrupt the light sleep easily. And of course, toileting needs and fear of accidents are a factor.
Good luck. You and your spouse have a hard job...

She could hurt herself by climbing and going over barricades. She needs 24/7 supervision, and you and your husband will not get any sleep unless you can get (hire) someone to come in and sit with her at night to watch over her, help her go to the bathroom and follow her around to make sure she doesn't hurt herself. Would your mother accept that, and does she have the financial means to pay for it? Have her sleep with Depends, if she will do it, and put a disposable pad under her, in case of accidents. If she leaves the house, or does things in the kitchen, she could be in greater danger, it could put you and your husband in danger. Lock up sharp objects like knives and scissors. If she leaves the house, she could get lost. My mother was a "wanderer." She was in a memory care facility and had to be in a locked area while she was still mobile.

My personal opinion is that it it time to place her in a memory care facility. She could fall and injure herself climbing, she could start messing with the stove and burn herself or burn down the house, she could wander out into the street and get lost or get injured. It seems she needs 24 hour care and supervision, and you and your partner need to be able to sleep knowing she is safe. Keeping her safe is far more important than keeping her home.

So, you all sleep upstairs? And you have something at the foot of the stairs to try to keep her from going up the stairs during the day? What is at the top of the stairs to keep her from falling down the stairs? Sorry if I'm just reading this wrong and being dense!

She climbed the side railing from a chair? Wow! She's like my 2 yo grandson. Inventive and no fear!

The odd questions are pretty run of the mill with dementia, as I'm sure you know. My friend's mom got stuck on Thanksgiving. She was always worried about the turkey.

Does she need to come out of her room at night to use the bathroom or does she have one in her room? If she doesn't need to come out, I'd put a baby gate across her doorway to keep her in there. I like the ones that are metal and you install them into the wall. Or I've seen in the nursing home where my MIL, a cloth gate that keeps the patient in AND keeps other wandering patients out.

If the environment is "baby proofed" and you've done your best at making it safe and escape proof as can be expected, then please stop worrying about her falling. The fact is, at some point, she WILL fall. Just about guaranteed. They fall in nursing homes, at the hospital, and at home. Not unusual at all. But you can't be all stressed out about it. Not healthy for you.

We're you in my house recently? ! My mum is 86 and I had to stop counting how many times up and down the stairs (stopped at 27, only driving me loopy) I've removed step stools, chair locations, added bright motion sensor lights to perhaps jar her, keep her suite warmer, even open a window in area where she does not like to cold. I feel your pain! Thanks for posting

Jessicat: Imho, perhaps you will either have to hire a sitter to watch your mother or your mother will have to be housed in facility accommodations.

Maybe a modified dutchdoor to her room with a simple alarm could be helpful.
Sorry you're going through this.
I had to have a door to a basement bathroom replaced with a lockable one with a pet door. This prevented my husband from sifting the kitty litter with his hands.