i would probably try taking tank off, taking battery out, using qtip with pga or rubbing alcohol to clean inside the 510 connection on the mod, including firing pin... set that aside to air dry... take tank apart, remove coil, make sure no juice down inside base (swab with dry qtip, if so) then put coil back in (make sure it is just finger tight, don't over tighten or you can deform the o-ring on bottom of coil and compromise seal), reassemble tank and put back on mod, put battery back in and fire it up... it sounds like for some reason it is not making a connection or making an intermittent connection... when it does not fire, what is showing on the screen - or does screen go blank?
which coil are you using and what kind of battery do you have in it?