I have the same issue and a different answer for you.
Yes you really should get someone in to fix it who is a pro but there is no harm having a good idea what level of work you are paying for before hand.
I have had this issue before and if the flames are lifting off the burners "reaching for air they can't get" then the unit is starved for air. You have tested it with the inner cover off and it worked fine so after putting the cover back on it went out you can deduct that it is not getting the air it needs to produce a good strong flame.
The inner flue is the air inlet pipe and the outer flue is the exhaust gases pipe. The exhaust gases also heat up the air to reduce condensation (caused by two highly contrasting temperatures passing through the unit) and also help the burning process (nice warm air coming in). so if your flue is quite long like mine you can deduct that the inner flue join may have come apart and the unit is sucking in exhaust gases that it has just expelled (instead of air) from the outer flue pipe putting the flame out.
I had this issue before and a service engineer fixed it so I watched him and asked questions. It cost me £60 for this simple service.
If you have isolated your unit and the outer flue is already apart it wouldn't do you any harm to have a look and see if the inner flue has come apart and if it has, push it back together and tighten the joining clamp. Then tighten the outer flue. Also duct tape is good for making sure your outer flue is air tight to stop the noxious exhaust gases from escaping into your house.
Don't put it on your inner flue join though as the heat may melt the glue and block your exhaust flue.
I suggest after you have put it all back together again that you get someone in to inspect your work and test it for exhaust gas leaks before you run it for any serious length of time, but get a price from them first so they don't rip you off.
Again, only do this if you are competent.
Randy
November 2007