Damn, that's good to know. This IC looked interesting on paper.
Reading the datasheet, we can see it's got quite a few different modes of operation. Between the soft-start feature, the "down mode", "pass-through", bust mode and synchronous mode... eek, there's probably a lot of cases, depending on how Vin and Vout relate, to make it go bonkers. In your case, I'm guessing it's probably stuck cycling between two of those modes (or more) in an unexpected way. This IC looks like a bunch of good ideas gone bad.
Not sure what you can do to get something reliable, short of switching to another boost converter altogether. Maybe select one of the Linear boost converters that have a burst mode and very low quiescent current (although this one will be hard to beat). Never had any problem with them.
A zener diode at the output is probably a bit pointless. It may protect your circuit but with the common Zener voltages of 3.6V and 3.9V (off the top of my head), you are likely to be in the diode knee most of the time, wasting unnecessary current... and even if that protects your circuit, I'm not even sure this would get the IC out of this weird mode when it happens, so either way, your device would probably not work properly. Maybe adding a second voltage supervisor at the output with a threshold of say 4V (if 4V is still safe for your circuit), that would disable the boost converter when getting higher than this. But that may just get it into an infinite loop of starting and disabling... and it starts getting a bit much for just one converter. Sucks.