I build the stable lvl 2 and the blueprint is still in my crafts and constructions. I haven't thought much of it since but when I try to use Stable lvl 3 blueprints, they never show up and they are no longer in my inventory. Is there something I can do to fix this issue?

Without seeing your constructions tab, I can't be sure what the issue is, but what this sounds like to me, would be that you already built Stable 3.. Check Manor -> Buildings, it will tell youw which level the building is. 

Firstly, when you build something, the blueprint for the building you currently have built vanishes, but you still see the prior levels. In the comments on the right side, it will say "You already have a structure of a higher level". If I'm right you should see Stable 2 in the constructions saying that, but no lvl 3, because that's the current active building.

The second reason why I think you may have built Stable 3 already is that higher lvl blueprints you have researched always show up in your construction tab, no matter how many levels below it you currently are. So this means if you did learn stable 3, it would be there, no matter if you built or didnt build lvl 2 yet. It would also show lvl 4 and 5 if you had used the blueprints for those already

Thirdly, you can upgrade building constructions by using another blueprint. This reduces the amount of silver needed to build the building. Sadly this also still works if you have the building already. So, let's assume I'm right and you have Stable 3, you then used another blueprint for it, which would have reduced the silver cost for it, but since it's already built, you didn't see this.. it would be itneresting what it said when you used the blueprint. If you learn a new blueprint, it will say that it was "added" to the library. If you already had it in your constructions, it will say that you "upgraded" the blueprint.

Sorry, I don't know how to phrase all this so it's less confusing, I hope you get what I'm saying =P

EDIT: I just counted your stable.. Unless I miscounted you have 68 pets - Stable lvl 2 only fits up to 50. Points yet again to Stable 3 being up already.