"Recently, I've noticed the plaster in the same area starting to bubble and crack. I opened the access panel to the tub and didn't see any obvious signs of water. Am I missing the leak?

Check tun caulking and the overflow gasket.

These are two common placers for leaks in tubs.

New water is damaging the plaster.

Once of the first uses of gypsum boards (similar to drywall) was in 16 inch x 48 inch panels that replaced wood lathe for 2 coat plaster work.
Wood lath took three coats to finish a wall, gypsum lathe replaced the wood and the first coat of plaster.

I'm thinking perhaps the repair materials were not up to the task, or the substrate had not been properly dealt with and made ready to take the patching compound.
The water-damaged stuff needed to be scraped away to a solid base, and then sealed with bonding agent (Link, or Plasterweld) to be sure it was sound. You can't patch plaster onto a friable substrate.
Casey