I have spotted cucumber beetles that eat the leaves of my plants. I read that eventually, their larvae will eat the roots of my plants.

I have tried neem oil, traps, and Sevin's spray, and the latter two seem to have kept them from eating the last remaining leaf (!) on my new pear tree, but I still see them occasionally on other plants, even though I sprayed everything.

Should I be concerned about seeing a cucumber beetle every few days? If so, how can I get rid of them?

To use a military metaphor, you are trying to stop a Tiger tank with a Boys anti-tank rifle.
Neem oil is completely ineffective as an insecticide in the traditional sense, traps work on some insects but not on others and Sevin contains possibly the weakest pyrethroid insecticide available on the market.

Diabrotica beetles are tough, extremely tough. Just ask corn farmers: if they could get rid of them using neem oil they would have bought the entire production for the past decades. To use another military metaphor, to kill them you need to either use a 17-lbs anti tank gun or call in an air strike, and these would be serious insecticides: malathion, imidacloprid, permethrin... it's up to you to decide what you feel comfortable handling.
Anything else is just ineffective against these beasts.