I once lived in a tiny little loft apartment with a no pets policy. I was all by myself in a strange new world and got a kitten to keep my company. Landlord didn't officially care the cat was there until there was some drama played out between him and my family.
Long story short, the landlord used the cat and my neighbors dumping of trash (I lived in the top level of a house, the guy below was a real trashy guy lol, no pun intended) as the reason to start an eviction process.
I was already on my way out of that dump and never had to look back at the potential eviction, but that's my point.
A landlord may not mind a small animal, and can even enjoy or talk to you about them, BUT!! if you don't pay rent on time and are somehow breaking some other big lease agreement... when it comes down to it, you ARE breaking the lease agreement, and it's one more nail in the coffin to get you kicked out of their property by eviction and possibly pay damages.