I had to use Fluke repair once many years ago and they were fast.
My Fluke 8060 has a chronic problem with the "zebra" connector between the LCD glass and the main board.
I have replacements but can usually fix it by taking the meter apart and cleaning both contact faces with a dry Q-tip.
My 8060 has been all over the US and Canada with me.
Paul - If you can find a good one on ebay score an old Fluke 8050A.
The display is usually what fails on those.
I've seen some really cool retrofits I might try on my 4th unit which needs one.
The Fluke 8050A one of the best bench "multimeters" for audio AC measurements since the true RMS section has some decent bandwidth and dynamic range.
For dB measurements they're accurate as hell.
The relative everything function and conductance are nice features too.
I have three plus a parts unit.
IMHO the AC-powered units are the best since the battery-option ones do require semi-working internal NiCds to operate.