If a reg is cutting out, it's probably going into thermal overload and shutting down. The way a linear regulator works is by taking any voltage above the setpoint (in this case, 5V) and wasting it as heat. That heat needs to be removed from the device, or it builds up and the chip will shut down to prevent you from frying it. A reg rated for 2A should be able to handle 2A continuously, but that usually assumes that you're using a heatsink to help reject the heat buildup. When you build a mod that doesn't use a heatsink, then enclose the chip in a sealed plastic box (or even worse, encase it in glue), then the heat cannot dissipate quickly enough, builds up, and shuts down the chip. Whether this is an issue depends a lot on how you assemble your mod and your vaping habits.
Adding even a small heatsink to a 2A chip will probably allow it to perform better than a 3A chip without a heatsink. Perhaps MV should consider carrying stick-on ramsinks like
these for just such a purpose.
