From your log I'd say that is the bug I fixed earlier today (see SVN thread). Basically the situation here is that Republic has lots of benefits from buildings it enables, and a larger city limit than Monarchy. However, the Israeli civ is not really suffering much from city limit unhappiness (its happyness is basically ok even in Monarchy). So what happens when it's in Monarchy is that it evaluates Republic as much better (small amount only from the city limit change, but large amounts from enabled buildings), so it switches to Republic (it does this in your log). However, when it gets to Republic, the bug means it no longer sees the benefit of the buildings it enabled (Forum etc.), and Monarchy looks more attractive than Republic without that benefit so it switches back.
This situation would not last if it grew a bit more since the city limit penalty from Monarchy would start to sting more, but as it is, it's in the 'dither zone' and the bug makes it oscillate between them so it never gets out of it.
Try with the latest SVN - you should see it switch to Republic and stay there within a few turns.