cat received vaccine 1 week ago, today he's not keeping food down

My 9 year old indoor cat was vaccinated a week ago. The last time he was vaccinated was 4 years ago, shortly after I adopted him. In the afternoon after his shots he hid under the bed, wasn't hungry, and he didn't keep down the little he ate. He was fine the next day, so he seemed to be having a normal post-vaccine reaction.

However for the past 24 hours he has not been keeping food down again. Other than that, he's acting like everything is normal - good appetite, no hiding, sitting in his usual spots, cuddling, he's active and alert. After he didn't keep down last night's meal, I've been giving him small amounts of food at more frequent intervals. I also tried Purina One Sensitive Systems food last night instead of his regular Iams for Mature Cats, hoping is would be easier on his stomach. He seemed to be better yesterday evening, but after I giving him a little more when I woke too early this morning, he didn't keep that down.

Is it normal for cats to have stomach problems again, a week after vaccines?

No, this doesn't sound like it's vaccine related to me.  Sometimes cats just get a "bug".  (sometimes literally they eat a bug which doesn't agree with them)

If you're feeding kibble, and you switched to the Sensitive Stomach, even THAT can cause an upset stomach, if you switch all at once, especially if he has a sensitive tummy anyway.  You might try mixing the two foods together and see how he does.  Or see if he'll eat some canned food...Maybe Fancy Feast Classics.  Most cats likek those.  If the vomiting continues, though, it might be time for another Vet visit.

Thanks! Phineas is back to normal now. Must have been a 1-day thing, perhaps he ate a bug.