There are gonna be a lot of variables to determine brass life. I have shot a few cases at least 6 times, so that's definitely possible. Most of them I have only shot once so far since I have 100. 3 firings is really low so something might be wrong. Mod only fixes case necks getting destroyed.
- brass manufacturer: the ones I shot 6 times were winchester for what it's worth. The rest of my cases are Norma which are also quite good. Federal are known to be crap. Remington I think are fine. That said, one of my Norma cases (once fired) cracked after only one shot by me (so 2 total), but in an m96. Defects do happen.
-rifle chamber: While in general semi automatics are known for generous chambers, I have found it quite easy to resize my brass from this rifle, and they don't grow too much with each sizing. Other rifles may have more generous chambers and stretch the brass more, reducing life. I measured my cases, and they started at 2.135 and 2.1365 and ended at 2.1435 and 2.144 respectively after full length sizing, so growing . While this is significant growth, it is quite reasonable, whereas, for example, my 7.5x54 MAS cases will grow 0.02" if full length resized.!
-load: full power loads will stress the brass more, especially "newer" loads with powders in the 4831 speed class, which will generate higher pressures for longer in 6.5x55 compared to 4064/4895/varget
-resizing aggressiveness: neck sizing tends to preserve brass life, but is inadvisable in a semi auto. You can size some rounds by partially pushing back the shoulder (i.e. unscrew the sizing die a bit), and see if they feed easily, this will help preserve brass life at the cost of reliability. I always full length resize for semi autos.
-less likely : defective shell plate or die which is pushing shoulder back excessively
It is important to check all rifle cases for incipient case head separation before loading them. This is easily done by straightening out a paperclip and making a slight hook in the end, then running it up and down the inside of the case to feel for a ledge or a burr (basically where your cases failed, you are looking for a "step" that indicates the brass there has thinned). CHS is not a big deal in bolt actions, but can send gas (and other stuff) flying into you in semi-autos, so it is especially important to check.
Since you only had one case separate (I assume), check all other fired cases for cracks on the outside, and for this step on the inside. If not present, it may have been a brass defect. If there, it is almost certainly one or more of the factors above. If chamber size/headspace is excessive, you will want to get that looked that, if it is just "generous", then the best thing to do would be bumping the shoulder less.