Hi Meza,
I'm thinking that your cat has a collar with a magnet?
and that this operates a reed-switch?
and that the reed-switch operates some kind of latch?
Hopefully to let only your cat through the cat-flap.
You said it is simple,
and you want something simple to try to hold the latch
a bit longer, cos your cat doesn't come straight in.
How about trying an electrolytic across the latch-coil?
Maybe 100 MFD just to see how long it will hold the
latch.
If you find that it wants more than 5000 MFD, then
maybe this method might not be good for the reed switch.
Because it would take quite a surge, but then as its a
battery, maybe the reed switch will be ok.
See how it goes, let us know either way,
Cheers, John