A surge protector won't help with this--they stop too-high voltage, they can't do anything about too-low voltage.

There are power stabilizers that will probably address what you are seeing. In a sense they're baby UPSes but they're only good for a second or so. The advantage they have over a true UPS is there is no battery inside to wear out. A true UPS contains batteries that get old and cease to deliver the goods.

If you do get a true UPS get one that has built-in self-testing. Manual testing is a pain and even if you do it you're liable to find out the hard way that the batteries aren't up to it--by having your machine do an unexpected shutdown.