Is there a way to "repair" or stop a small hole in a shade netting car port from getting bigger?
Depends in part on why it has a hole.
If it's old and getting degraded by the sun, it will just tear somewhere else, and wholesale replacement is going to be the best option.
If it was cut by something but is in generally good shape, you can sew a patch to it, overlapping the holed/torn area. You MAY also be able to just melt the edges if it's a small hole.