If you cover your pit or anything for that matter, you usually will find evidence of water on the top surfaces of the covered item as well as the top underside of the cover.. The longer the cover is left on the

 worse it gets - to a point. That's with a good cover w/o any tears or leaking seams.  Arid climates excluded.

  There is one cover manufacturer that recommends removing the cover on a regular basis to dry things out. That applies to their vented covers as well.  They go on to state their spacer bags should be used

 between the top of the pit & cover to generate a breathable airspace, even with their vented covers.

 For years I have always placed something between the pit & cover to generate an breathable air space & offset the flat top that tends hold water (dew & rain). 

 Depending on the pit, the "something" has ranged from a rounded corner & edged 2 x 6, sanded & urethaned  with silicone feet for additional height & air space, to a 2" plastic pipe with the ends cut @ 45º &

 the edges rounded so as to protect the cover. This  is screwed to sections of 1 X 3 pvc trim with silicone feet a few inches long to support pipe. The result is a super air space with an excellent slant to the cover..

 The down side is dealing with the "something". It's easy to get used to.  The benefits have been rewarding especially for my Weber gasser that is rarely used.

 I used to never cover my pits, finding with several of them some would sit idle for lengthy periods accumulating some nasty deposits that were a chore to remove encroaching on cooking time.
 
 The domed top/air space addition has been a plus for me..

I've had covers by Mel ever since I've had pits.
Never had any issuer with moisture getting under.
Granted, TX and NM are fairly dry but pits have had rain and snow on them.
Even had a cover for my log splitter that was always exposed to the weather and had no issues.
Maybe if I lived in a more wet area I could have issues.