When a blade starts to dull, I put it in my second rotary cutter which is a cheapy I bought and is red so easy to tell apart from my Clover one then I use it for a while on trimming up poly batting or cutting paper. This I do on the flip side (metric and so no use to me!) of my mat. I understand that a dull blade damages your mat so is false economy to carry on using it when it's dull. You're also more likely to cut yourself with a dull blade as you have to apply more pressure so it's more likely to slip.
In the same way that you shouldn't use your fabric scissors on poly batting, you shouldn't use your good blades either because it dulls them as cutting paper would. I do save the plastic case and put it in there before throwing away.
I'll try your flipping over idea Tiffany, I didn't know that was possible so thanks! :-D