Gallup has a new piece out by Andrew Dugan about a supposed "second term curse," and noting that every second-term president in the Gallup era except for Reagan and Clinton had lower approval ratings averages in their second term than their first term.
A lot of this may only be regression to the mean. That is, if presidential approval is a coin flip set to an average around 55% over the long haul, then what you're going to find is that presidents with a first-term average north of that are going to fall back -- and those who fell short of it will rally. And guess what? The two (of seven in Gallup's summary) who improved were the two who, up to now, had the lowest first-term rankings. Reagan and Clinton tied at 50% average Gallup approval in their first terms; they held the record for re-election, until Barack Obama at 49% just edged past it.
One question is what would have happened to Jimmy Carter, Gerald Ford, and George H.W. Bush if they had been re-elected. It's possible they were just bad at the job (surely Carter was) and would have been very unpopular no matter what -- but it's also possible that they would have produced at least one addition to the "plus" side of things.
But Gallup ignores them by only looking at two-term presidents. And guess what? Most two-term presidents were pretty popular in their first terms -- that's how they got re-elected!
That's not to say that there's nothing to the possibility that second terms can be rough on presidents. But if what you're doing is looking at the numbers, you need to be careful about what they're really telling us.
Which is mostly to avoid a terrible recession or a war which appears pointless and hopeless. Oh, other things matter too; Clinton does better than Reagan, for example, mainly because of those other things. But the big hits, the stuff that chases first term presidents out of office or makes second term presidents unpopular, are mostly terrible economies or awful wars. But outside of Watergate, that's what's going to really cripple a president, sending his approval ratings south of 40% for an extended period.
The question is whether there's something inherent in second terms that leads to trouble, and that's a big and complicated question. But we're not going to get at it with this kind of analysis.