If you have Invisigrip on the fabric side of your ruler, the answer is probably in your cutting technique. Many people put way too much pressure on their ruler when cutting, causing slippage. Try for a completely vertical cutter that is aligned with the ruler, not tilted in either direction or canted toward or away from the ruler. The key is to exactly follow the ruler while putting almost no pressure on it with the cutter.
An ergonomic cutter, such as a Martelli may put your hand in a more comfortable position and allow more control over the cutter. I works for me.
I'd also recommend a book "Judy Martin's Ultimate Rotary Cutting Reference" as a good one to have around and learn from.
The rest is just practice, and a lot of it.
Good luck!