If our original lease states “One time nonrefundable pet fee” and we are up to renew our lease for another year, can our landlord charge us again for the fee?

If this is a lease renewal--i.e. the same lease is still in effect, with just the start and end dates updated--then no:since it's the same lease, the landlord is bound by the representation that the fee was one-time. But landlords are allowed to change lease terms and put out new leases after an old one expires, rather than to renew the lease as is: if this came to litigation and a judge believed that this was a new lease, with new terms, he might allow a new fee. There is not, unfortunately, a single right or wrong answer: it will depend on what exactly you were sent, how the "renewal" was described or positioned, and whether the landlord could convincingly (if the language of whatever you were sent supports it) argue that this a new lease, with new terms.

The above said, I suspect that if the document again called it a "one time fee" that a judge would, even if the landlord called this a new lease, find that you've already paid your "one time fee." But if the document used different langauge and dropped the phrase "one time" to simply call it a "pet fee," a judge very well might conclude that the landlord has changed its policy--which it is allowed to do--and is now charging an annual fee, which they may.