First check that all the connections are good, starting at the plug and socket (including the 'receptacles' in the socket outlet, which sometimes open up and don't grip the plug so well). Also check all the connections in the starter. If they are all ok then it's either dust or moisture inside the starter, or it could be dirty contacts. It might be possible to strip the starter down and polish the contacts with some very fine wet/dry paper. If not then you might have to buy a new starter.
I'm not sure about the DeWalt, but there may be an adjustment for the trip current in the starter which you could try increasing a little.
In any case, it would be well worth reading 9fingers post stickied at the top to give yourself some background info before you start your diagnostics, esp p14-18.