MOSFET mechanism of failure: was it the heat?
I think your soft start may be your problem. Are the FET's on heatsinks? People usually don't do this because received wisdom is that a FET as a switch is not dissipating heat. But I had an experience (many years ago, also with an IRF series) that was quite educational.

Basically our system had IRF520's (from memory) switching up to 3A or so DC. They were "protected" by a 3.15A fuse and everything had been fine for years. One day (due to an unfortunate accident) we left one of the FET's passing 3A or so (in fact the cable resistance was just enough to stop the fuse blowing). When we came back there was a lot of smoke and only the fact that the containing equipment was flame-retardent prevented a very nasty fire. The board was an ugly charred mess.

I was tasked with the investigation and re-design. It turned out that thermal instability was the problem. Basically, Rds on those FET's rises with temperature. So when they are switching in conditions where they are just OK, thermally - quite soon they are not. 

For the redesign, I took several remedial actions - "belt and braces" was in order:


used FET's with even lower Rds 
mounted them on a big chunk of copper bar (heatsink)
beefed up the PCB by using a 16/0.2 wire to get the DC off the board.


The result was heavily tested, did well, and is still in use (has been more almost 2 decades).

This is a bit different to your situation, but the fact that you are "soft starting" over 100ms,  while the load has an initial current of almost 3.8A, and a time constant of 9ms (5CR is then 45ms) means your FET is getting quite some thermal stress. I don't fully follow your graph, but I wouldn't trust this situation. Switching FET's are not really designed to handle much thermal stress, the general idea is that they slam on and never have much volts across them. But the moment there are even a small number of W getting dissipated - the story can change. 

I would consider getting rid of the soft start if your system allows it. (What is it really achieving anyway, if the load is a series CR? What is the initial resistance of the FET relative to 9 ohms?). Also beef up the thermal protection on the FET. Also you might look for any data on the thermal behaviour of Rds. (EDIT - I just looked and saw that indeed it rises quite sharply with T.)