It is perhaps tipping because it is top heavy.

Fill it less than halfway with something heavy... sand, glass chips, river rocks, gravel, coins.

I've used museum putty (in a museum) and it works great. It's not a guarantee your fragile items won't end up in pieces, but it is a worthwhile precaution. You don't usually need a whole lot, but if it's going to be routinely knocked at by your cat then don't be shy with it. I helped an old roommate secure a shot glass collection the same way when he had a neighbor with a jacked up truck that would shake the walls of their crappy apartment building- no more rattling.

Yes museum putty - available at any Loewes or Home Depot near the earthquake safety supplies. It's sort of like high quality Blu-Tak, and it works really well.

I've used it for vases and lamps. There have been a couple of times when someone banged into a table or shelf, and I'm sure the vase/lamp was saved by the museum putty. If your cat were to really run into the vase, then it might fall even with the museum putty.

I live in an earthquake zone, use Museum Gel (the clear version of Museum putty) to secure breakable objects. Nothing broke during the last earthquake.

You can also get it at the Container Store.

I use museum wax in my studio to keep silly people from picking up covered jars and breaking the lids... :) So if it can stand silly people in retail stores.. it might just be able to stand your kitty!

I have the same problem with my cat. But Will the putty or gel damage the surface of the item that you are placing the vase on?
Thanks

The putty or gel is designed not to damage most household surfaces, including finished wood tables.

I'd still also go with p(too)'s advice to put something heavy in the bottom. It can't hurt, and removing any wiggle will make the vase less fascinating to the cat.

Can it be used on porous (fired) clay, or will it leave an oily mark?

Thanks Wende.