Diagnosis needed
 

'99 std convertible loses power and starts cutting out after a few miles in a steep climb or on hard acceleration. Happens at any temperature--50 to 100 degrees. On stopping, car will idle normally. After stopping and shutting down motor for 10 minutes, car will resume normal performance in steep climb for 1 to 2 miles then cuts out again. The loss of power does not always happen on the same climb. The performance is normal on level driving. Car has 20,000 miles and was not driven for 18 months. Gas tank was cleaned and has new filters.
Three repair shops and a Ford dealer cannot find problem.
Any suggestions?

Did they replace the fuel pump when they cleaned the tank? Was the baffle still tacked on.
It sounds like maybe a weak pump ( will not handle the extra load when climbing ) or the pick-up is not immersed in fuel when climbing. Just guessing here.