It turns out that, under certain circumstances, G1 goes into "mixed GC" phase and does not come out of it in a timely manner. In some cases, several mixed GCs collect no old regions but are still considered "mixed". This, unfortunately, causes a serious issue: while we're in mixed GC mode we do not allow a new conc mark cycle to start. So, we have seen cases where a series of mixed GCs take place, the next cycle starts too late, and we end up with an evac failure / Full GC.
Many thanks to Charlie Hunt for discovering this.