I have an older model Foodsaver. The machine will

This is likely happening because the unit cannot detect that a vacuum has formed, and the gaskets around the vacuum channel are the probable culprit. The Foodsaver gaskets will deform and/or dry out with time, just like in any device, but you don't necessarily have to replace them. I've tried this inexpensive solution on my own Foodsaver V2490, and it works perfectly.
Buy some food-grade silicone grease and apply it to both the upper and lower gaskets. I remove the gaskets and coat both sides with a thin layer of grease before replacing them in their respective channels. And since this grease will be absorbed and/or dry out with time, you will have to do this occasionally, so I also flip the gaskets (i.e. turn them over) whenever I apply the grease.
You can buy a 2 oz container of silicone grease at any dive store, or you can buy it over the Internet by searching for "Trident silicone grease".
This is a link where you can buy it for around $7.00:
Dolphin Dive Center
I do not work at this dive center, but I am a scuba diver and already had some grease that I use for the numerous rubber gaskets in my gear. The 2 oz. jar will last you several years, and you will find many other uses for it around the house since the grease will last longer than a spray.