I have been a property manager for 10 years in the state of Oregon. Laws vary from state to stae so be careful not to heed anyones advice who is just guessing - especially from another state.
Your landlord may or may not be in the right. Read your lease. It will spell out exactly what you are required to do in order to have a pet in your household. Do you follow the lease? In Oregon there is a landlord/tenant hotline where you can get free information. Check your blue pages of your phone book, do a search on line, or call information. I'm sure your state has one too. There's also Legal Aid here in Oregon and your state might have one too. This is also free information.
If I were you I would talk to the landlord and ask if you could pay the rent, etc. and not the pet deposit. Have your checkbook in hand ready to write a check. Tell her/him what you know about the pet deposit (after having called and found out the legalities). Even if it is not in your favor. The best thing is to leave out emotions and keep your anger in check. If you found out that the landlord is right, you can ask to have the deposit waived based on length of tenancy. If there is no way that they are willing to waive the deposit and you don't have the money, ask for a payment arragement starting by putting $25 towards it that day. Then stick to the arrangement.
Without knowing all the facts, I cannot tell if the landlord is being unreasonable or not. Your lease will answer that for you. Regardless of your lease, your landlord is a person and every person responds well to open communication without blaming.
If I were the landlord at your property, I would be VERY open to receiving what is owed (rent, etc.) short the pet fee/deposit. But, it would require a conversation with you and an understanding of where you are coming from. If I could see that you know you are responsible for what is owed and would not fight me on it, I would be more apt to make arrangements for any other monies owing. Rent is very important to collect. Landlords must delcare all monies owing on legal documents sent to you so that IF they need to take you to court they can ask the judge for what is owed.