Usually there isn't a problem with depositing money in the account.
The one thing I will add is that if your father is in agreement and if he is able to make a trip to the bank with you depending on his health in the future....you might consider adding your name to the bank account as a joint account.
Our attorney advised me to do that with my mother and I can't tell you how helpful it was! Any bank business I needed to do for Mom when she wasn't able was no problem, because my name was on the account. Even though I was POA, it still made it much less cumbersome conducting bank business.
Just a thought and good luck with the bank.
* Freedom has a taste the protected will never know *