A couple of years ago, there was a recall on a part that a Company had to come out and replace. I had never had a problem with the furnace for 8 years. A short time later, I started having problems with ignition failure. I had a part replaced and a licensed Company went over everything and said it was all OK.
Now, the furnace is beginning to experience the same problem intermittantly. Occasionally, the green light in the window will show one flash. I back off the thermostat to where it clicks, and return it to the desired temperature, it will begin its heating cycle again. Sometime this takes a couple of times before it will heat. It will work maybe a day or two, then fail to ignite again.

I've paid good money to have it professionally repaired, but it is now doing the same things again and it hasn't been even a year since it was last serviced. They removed a part from the burner and washed it off in the sink, vacuumed everything out, re installed the part and said it should be OK.

Is there something I can do?

Who said this (re installed the part and said it should be OK)?
Try cleaning the flame sensor with steel wool.