That's very unusual for a renewal. Many times prospective tenants who are self-employed/contractor or retired will be required to provide bank statements showing steady income or a certain amount of cash in the bank to qualify for new rentals. (this varies widely from owner to owner, or management company)
A> They're refinancing or selling the property, and the bank or buyer is asking for it because of shitty landlord bookkeeping.
B> New management company is taking over, many reasons come into play there... don't even know where to start.
C> You've not been 100% on time with rent recently, and they think they can fill your spot with a more qualified tenant.
As a former (Texas) landlord, I'd say no. Worst they can do is ask you to leave at the end of your lease. In Texas, the landlord has to give you at least as much notice of new terms for renewal as is required from you to give notice to leave. Typically, I'd give minimum six weeks written notice for any change in terms prior to renewal, more if big changes are made.
Laws vary from state to state, but the above is almost universal. You'll need to check with your state's landlord-tenant site for more information.
If it comes down to it, and you want to stay there despite this, all you need to show them IMO is name and either end balance OR deposits (if deposits only they might ask for three or more statements)