The immune system killing T cells can recognize cells that have abnormal proteins...mutated proteins, virally infected proteins, etc. Your immune system wipes out a lot of cancer-like cells as they arise.
When you have a tumor, I think we are looking not so much a short coming of a normal immune system, but instead the cell that "got away" because it acquired mechanisms to "trick" the immune system into leaving it alone. The immune system is quite complex and it works most of the time very well, but a sneaky cell could come across "loopholes" and "trickery" and therefore escape the immune system.
Also, some aspects of the innate immune system might even stimulate a tumor...Tumor infliltrating lymphocytes...drawn to the tumor...maybe to fight it, but then these immune cells release substances that actually help the tumor to grow more...
Some cancer cells just don't look different enough to be sniffed out by the immune system as anything abnormal.
There are laboratory-medical interventions to hyperactivate the immune system, and these might help against some forms of cancer--melanoma. But for a GIST...your immune system may have gotten rid of other GIST like cells in the past, but the one that became the primary tumor was the one that found a way to hide from the immune system.
GIST Support Wiki