I burned through 4-5 cheaper DMMs in the $20 to $40 range before eventually getting Flukes. Some of the cheaper ones died completely, others didn't die completely but stopped working reliably. I now have 3 Flukes.
Beyond reliability, one of the features I like most about Flukes is how fast they are. I can measure continuity and diodes very quickly which allows me to run through all the checks I need to do on a given board in less time. When checking shorts to ground on a long row of transistors, I can literally just run the probe across the back of them listening for a tone as I go. I haven't found a cheap DMM that can do that unless I go really slowly. If I'm checking 50 components on a board, saving a second or two per check matters.
The other feature I really like is the tone on diode check as it prevents needing to look at the meter for every test. It makes life much easier when testing pinball boards as the diode check is probably the most common test I use. Not all Flukes have the feature. My current favorite is the 117 as it includes the diode tone test as well as the AutoV which is nice when testing parts of a board that could be either AC or DC.
-Jay