Nate Silver suggests that Republican governors are unpopular due to their conservatism:
[J]ust a year ago, there were plenty of moderate Republican governors — most of them in liberal or moderate states, where they were often quite popular. Now there are almost none, save some borderline cases like Mr. Daniels and Mr. Herbert.
The unsurprising result is that Republicans now have a group of extremely unpopular governors — particularly Mr. Scott of Florida, Scott Walker of Wisconsin, John R. Kasich of Ohio and Paul R. LePage of Maine, all of whom have disapproval ratings exceeding 50 percent. Other Republican governors in crucial swing states like Michigan and Pennsylvania also have below-average ratings.
What Silver omits, though, is a more basic political fact: incumbents tend to be unpopular when the economy isn't performing well. Here are two graphs from Jim Stimson's Tides of Consent (previously reproduced by John Sides on The Monkey Cage) which show how approval ratings of governors and other public officials and institutions trend together and generally follow perceptions of the economy:
It's possible that the conservatism of the GOP governors is driving their approval ratings even lower than they otherwise would be, but a poor economy is difficult for every incumbent.