You certainly can gain health containers while rerolling items, as documented for example in this video. I never saw anyone losing them while rerolling.
I think that when rerolling, you lose no health containers for lost HP up items, and then gain HP for items gained, but I couldn't find any info about that, and didn't have any opportunity to test it myself.
Best Answer
Yes, it is possible, but very rare.
When rerolling your items, you do not lose any bonus health gained from items you previously held (though you do lose other stats, such as damage or speed). Since there are so many health-ups in the game, Chances are pretty good that rerolling will actually increase your health pool - you can see this simply by getting a lot of items and rerolling once.
Since you do not lose bonus health and instead gain more bonuses when rerolling, the only way to lose health on a reroll is if a new item in your collection decreases health. The only item I can think of that does this is Experimental Treatment, which randomly increases/decreases each of your stats. Occasionally ET will decease your health stat... however, when rerolling a lot of items at once, you might not see the decrease (again, since you might gain other items that increase your health at the same time). (Not to mention ET can't remove your last heart container.)
So in summary, the only way to lose health on a reroll is when you have more than 1 heart container and you reroll an item into an Experimental Treatment that randomly lowers your health, AND you don't get any other health-ups as part of the reroll. This situation is relatively rare, so in most cases you will not lose any health when rerolling.