I relinquished my power of attorney of my elderly mother. My mother is 94 and has been declared incompetent. Is this a breach of her duty?

No, a POA cannot hold back money needed to support the Principle. Actually, the POA should be paying all the bills and making sure Mom has enough to live on. I would call SS and tell them the POA is withholding money. Same for any pension.

Here is what you posted on your profile:

"I’m dealing with caring for my 94 old mother 24 hour caregiver is in an out and the only biological child and my brother adopted brother stole millions from my parents- fraud etc Which is causing a lot of stress in the house and now that my mom has vascular dementiaNot want to keep bringing up wipe my brother has done how do I keep the stress level anxiety to a bare minimum thank you"

Is your mother now impoverished from the fraud? If so, she may be in dire need of Medicaid to pay for her care. The financial PoA would need to be extremely careful that all expenditures have a paper trail so that she she can qualify (and the fraud may also be a problem in qualifying). Therefore, it would be no surprise that the FPoA would not be willing to hand out "petty" cash of any amount since it's harder to account for.

It may be useful to prepare and submit a monthly budget of your mother's expenses which can be reconciled at the end of successive months.
Such legitimate expenses with supporting receipts/statements should facilitate reimbursement as the POA must act in the party's interests as they would do for themselves if capable.
Drawing petty cash may not have enough supporting evidence of actual expenditure thus creating resistance to allow access to funds. Clearly, you need to ascertain the actual reason from the POA, so don't be afraid to ask the question.