The mechanic doesn't know why a 1999 Toyota RAV4 would lose power and die especially when the weather is bad without giving a check engine light?

I can't see when this question was posted, so probably already sorted it!

If by "bad weather" you mean wet and damp, you may look for a short somewhere in the electrical system. Condensation and dampness may be causing a short somewhere that when dry, just does not happen. Try turning on ignition, not running the engine, at night with no lights around. Move some wiring under the hood and you may see some arcing. It needs to be completely dark to see unless you have a particularly bad short. I had this on a car about 15 years ago and found it by accident just like this.