Honestly, I think new pet sites should release new features as often every few months depending on their developers schedule.

However, a game that is fully developed already does not need new features all the time. They can actually survive without new features all the time. New mini games, and/or features that are updated instead can enhance their gameplay elements more so.

Pet sites are able to survive a lot better when things aren't changed quite frequently, but some players do get bored when new things aren't released that often. However, you can't rush a developers process.

Upgrades and features take time to plan & develop, especially big time features.

Simple dailies like quests can be more beneficial to the player base rather than big time features as well, and keeps the game flowing with content in the long run too.
 
New features should come often enough to keep things fresh, but not so fast that players feel overwhelmed. I think small updates regularly and bigger features every few months can be good.
Predictable updates build trust and give players something to look forward to.
 
You can go slow and make each update feel bigger. Releasing a major feature every 2–3 months builds anticipation, gives time for polish, and lets players fully explore what’s already there before adding more complexity.