Jelly, 14 bytes

Œɠ>2i1œPŒgFµÐL

Try it online!

Takes input as a list of digits, outputs as a list. Outputs [] if the result is empty. The TIO footer converts to/from numbers to lists (and converts [] to 0)

Jelly, 14 bytes

Œɠ>2i1œPŒgFµÐL

Try it online!

Takes input as a list of digits, outputs as a list. Outputs [] if the result is empty. The TIO footer converts to/from numbers to lists (and converts [] to 0)

How it works

Œɠ>2i1œPŒgFµÐL - Main link. Takes a list of digits D on the left
           µÐL - Until a fixed point is reached, do the following:
Œɠ             -   Run lengths of equal adjacent elements
  >2           -   Greater than 2?
    i1         -   Find the first truthy index, i
        Œg     -   Group equal adjacent elements
      œP       -   Split, removing the element at the index i
          F    -   Flatten