The length of the rifle barrel is what'll kill it. A pistol dumps its internal pressures quickly - the short muzzle doesn't have to hold the pressure for more than a millisecond or two at most. A rifle on the other hand? The longer the barrel, the longer that period of time which the barrel has to hold the higher pressures. Most rifle cartridges also contain a slower-burning powder (to keep pressures at least somewhat constant as the bullet travels down the barrel), which only exacerbates things from a design perspective.
I think the duration of the high pressures is a second-order issue, behind the fact that most rifle rounds generate much higher pressures, period. A few examples:
Handgun rounds:
.380 ACP: 21,500 PSI
9mm: 34,800 PSI
.357 magnum: 35,000 PSI
.40: 35,000 PSI
.45 ACP: 21,000 PSI
Rifle rounds:
5.56mm: 62,366 PSI
.270: 65,000 PSI
.308: 62,000 PSI
.30-05: 60,200 PSI
I'm not aware of a single handgun round that is designed for more than 40,000 PSI, while most modern rifle rounds are in the 60,000+ PSI range. The lowest-pressure rifle round I'm aware of is the old .45-70 government, which still peaks at close to 30,000 PSI.
It's worth pointing out the Defense Distributed's Liberator fires the .380, a low-pressure round. The .45 would also be a good choice. Perhaps even better would be the .38 special and .44 special, which have max pressures around 14,000 PSI. Best of all would be some hybrid round which is loaded for low-pressure but is fired out of a casing designed for a high-pressure round. That would allow the casing to take more of the load and demand less of the plastic chamber.