Could this be a conflict with long exposures? Conceivably AF, too. The intervalometer will attempt to trigger capture every 5s wall time. If the combined time to AF seek, expose, and finish saving to card (etc) is >5s, you will skip a shot.
When the time comes, compare the price of a used 5d3 vs a shutter replacement on the 5d2, maybe you'll get a "free" upgrade :) Thanks for the kind words!