I increased the infill overlap value in Cura to 38%, bumped extrusion speed to 120%, raised temperature of printing, but there are still gaps. I am printing at Ultimaker 2 (not 2+) with ABS. Sliced with Cura is 15.02.1, since I cannot use more recent versions due them slicing my models incorrectly (Thread about that), but I've used this version for a while, and this issue is only developed relatively recently, so I am suspecting that something must be up with the printer itself.
It doesn't look like underextrusion (which is usual culprit of "stuff doesn't connect!"), though, since everything else is printing as expected and without any issues.