Why do Republicans think that Donald Trump being re-elected will save them ?

The Republicans in positions of power are intoxicated with the power and only want to stay in power. That's not necessarily a reflection on Republicans (real ones or the fake ones, aka Baby-trump followers). It mostly reflects all of human nature.

"The base" isn't really interested in any of the social issues to any large degree, they are basically just getting a kick out of believing their support of Baby-trump is agonizing to those who they feel have ignored them (and their kind) for so long. And, so in that sense they too feel a sense of power (finally) and they too are intoxicated with that; they won't let go.

And, the person commonly referred to as Baby-trump is basically engaged in a programming exercise. He sees a group of people who have been mismanaged by being ignored and saw a way to build quick market share. He's giving them what they crave and he has their instant endorsement. Even the fat man supporter who Baby-trump body-shamed loves the grossly obese Baby-trump even more now. Roger Ailes described his programming choice for building Fox News (and Entertainment) as a way to quickly reach a market of people who were not being served. He clearly stated that if liberals were the ones not being represented by the media, he would just as easily and unapologetically oriented Fox towards them. It's simply a game of numbers. Baby-trump is in a somewhat unique position of not having a personal interest in any of the issues he proclaims as his own. Like the middle school girl with raging hormones squirting estrogen all over the place, he just wants to be popular.

And, so he gives the Republicans and those who call themselves Republicans want they want (recognition) and they give him what he wants (undying and breathless loyalty and the feeling he is popular).