What should I do if Mom is in a bad mood and doesn't want company? Should I give her space and not visit?

One easy answer is 'yes'. If she doesn't want it, don't go. I'd say again that an easy way to keep contact is to send cards or postcards, even every day. They make a big impact on the receiving end in a facility, and don't normally offend someone who is looking for some peace of mind.

How long since Mom has seen her doctor? She may not be feeling well and could benefit from a doctor’s visit. What makes you think she is “giving up”? How old is she? Has she always suffered from depression? Does she live in a facility or in her own home? Does she get out among people? Have any hobbies?

All of us go through periods when we just just don’t want to be messed with. Respect her wishes and don’t visit. But keep contact with her with short phone calls. If it seems she’s getting worse, explain that you’re worried and will go with her for a chat with her doctor.