I'm not very good at debugging memory leaks, but I thought I'd share what I found so far hoping that others may have more luck.
I have a rather big and complex document (500 Kb SVG) containing many icons which I export individually. I noticed that after each export the inkscape task grabs about 5% of my total memory (512 Mb) and never releases it. This happens even if I export small bitmaps (64x64) and even if I export the same icon again and again. So, after exporting about 20 icons, all my memory and swap are eaten and the system grinds to a halt. Only killing Inkscape can revive it now.
I traced the export command and found that the memory grab happens in nr_arena_group_update called on the document's root (which, obviously, calls updates of all other arena items in the document) which is called from sp_export_get_rows. I could not track it further down but I suspect it's some unfreed memory in livarot. The amount of memory eaten in one export operation does not seem to depend on the resolution of the exported area but depends on its size (though not proportionally; it grabs about 7% if I export area 16 times bigger). During normal work it does not eat memory that fast.
It's not a recent thing; a build from early August has the same problem. However Inkscape 0.37 is OK, and by the way it takes 3 times less memory upon loading that document (5.5% vs 17%).
So if anyone can play with things like valgrind or electric fence, this is a very annoying bug which needs to be addressed.