It's normal for parties to lose support the longer they stay in the White House
That's a meaningless statement. The Federalist Party isn't entering their 226th consecutive year of majority rule, yeah, but they didn't decline because of fatigue. Thomas Jefferson (DR) defeated John Adams (F) for re-election. If Jefferson were running against Washington, he would have lost.
The Republicans are not entitled to more vote because the Democrats have been in office for 8 years. They need a candidate that white voters like more than Clinton by a margin greater than white voters preferred Romney to Obama.