With the exception of the 55-110 zoom (which a number of people have had touble with) I have found the H system to be extreemly ruggged and reliable. I've used my H1 and H2 in conditions that include sub-zero to desert heat, as well as in heavy rain, snow, and blowing sand, and never had an issue. Occasionally the camera needs to be rebooted, which simply involves removing the battery grip and reattaching it, which takes about 5 seconds.
As for back reliability, after two years of constant use of a Phase One P25 and P45 I can report that I've had more trouble over the years with MF film backs than with digital backs, and that includes a year with the Kodak DCS Pro Back before the first Phase purchase. Arctic to Africa, never a misstep.
I used the P45 in Antarctica last year and plan on bringing it (likely the new P45 Plus) and my H1 and H2 there again this coming February. It's a solid state device with no moving parts. Other than water damage or being dropped there's little that can go wrong. Some Phase MF backs have seen use in aerial cameras with hundreds of thousands of exposures, so there is no life span issue.
Leaf, Hassy and Sinar backs may prove to be as reliable, but I have no personal experience with them in extreeme conditions the way I do with Phase.