I'm using PM 3.55 on Android/ICS 4.04 on Samsung Galaxy Nexus, before 4.0.1 but I'm not sure whether that was the same as now:
If I press the button "getting emails" (globe button) without having an internet connection available (i.e. using Juice Defender which switche internet off, when screen is locked for saving battery), than all the bottom menu buttons disappear.
To get the buttons back, it is necessary to restart PM.
See the enclosed pictures - one as normal
pm_troubles1.jpg [ 166.01 KiB | Viewed 1358 times ]
and one after pressing the globe button without internet connection available
pm_troubles2.jpg [ 148.36 KiB | Viewed 1358 times ]
I dont know whether that is an ICS/Android-Problem or PM ones.