How old is your cat?
Has he been to the vet for this problem yet?
Dr Vicky is offline - she will be happy to help you when she comes on line so please be patient.
If he had a seizure problem when you got him, most likely he has epilepsy. Epileptic seizures are often triggered by stress. We don't see epilepsy as often in cats as we do in dogs, but I have seen a couple of cases in my years of practice where we thought it might be epilepsy (no found cause of the seizures). There are other causes of seizures in cats, but unless you do a lot of testing, including an MRI or CT scan, you might not know the exact cause. There are treatments for seizures, however.
If the seizuring has gotten worse recently, there is a medication that can be used to prevent them. The medication is called phenobarbital, and it is pretty inexpensive. You will need a prescription from the vet. The vet will want to examine your cat, and probably run some blood tests. They can then prescribe the phenobarbital. It is recommended to check the levels of phenobarbital after they take it for a month or so. This is needed to make sure they aren't getting too much, and it will let us know if we can increase the dose if the seizures are still occurring too often. The expense comes with the blood tests. In our office, initial blood work and a physical exam would run around 125.00. Of course, this will vary with the vet, state you live in, etc. The phenobarbital for a cat is really cheap, and most people can afford this medication.
Your vet shouldn't recommend putting him to sleep just yet. If they do, seek a second opinion. I would try to get him on phenobarbital, though, because of the concern with him having seizures on the stairs. He could really hurt himself one day!
Here is a website with information on seizures: http://www.marvistavet.com/html/seizure_disorder.html
And a site about seizures in cats specifically: http://www.cs.cmu.edu/People/lowekamp/feline_epilepsy.html
Let me know if you have more questions!