Some landlords charge an additional fee per pet, per month on top of the basic rent. This is also in addition to a one-time pet deposit. The reason for this is that it is expected that pets, will be destructive. Obviously there are a lot of exceptions to this, but I have seen plenty of tenants that neglect their pets and allow their pets to cause damage to other's property. There are plenty of horror stories from landlords out there that have rented to pet owners where the pet has destroyed their property.
As with everything in real estate pet fees and deposits are negotiable. Just because a contract says that a pet deposit is non-refundable does not always mean that is the case. With some landlords, if the tenant leaves the house or apartment in better condition that then received, the landlord may return the non-refundable pet deposit back to the tenant.
If I can be of any further help, please contact me.
Keller Williams Realty