You must be doin' research for an article...
The only re-useable chain link that we broke was one of the first generation Sach's 8 speed PowerLinks back in November of 1997. We were both standing in a full sprint when it let go. Not sure if a pin or side plate failed or if the chain went slack enough on the return run to come undone.
Since then, have primarily used the Forester SuperLink's (sold by tandem dealers, Lickton's and Branford bike - but Lickton's is the cheapest by far) on our drive chains and dispatched the PowerLinks to the duty on my personal bike an the timing chain. However, we have mended many other broken road and off-road tandem drive chains (almost always a Shimano chain) with spare PowerLinks that I keep in my patch kits / saddle packs.
As for problems, the PowerLinks will bind-up if they are not kept reasonably clean. Folks who use wet chain lubes that don't routinely clean their chains will almost always have a hard time trying to remove a PowerLink as the trapped grit prevents the side plates from compressing enough to slip off the pins. A shot of WD-40 will usually flush out the crud and then the links come right off.
In my view, the re-usable chain links have evolved to a point where there is no reason not to use them, short of track racing. Forester makes the SuperLink in 8, 9 and now 10 speed varieties. Wipperman's Conex connector is also available in a 10 speed model, along with 9 speed. SRAM has the PowerLink (8 speed) and PowerLink II (9 speed) and they work just fine, just not as nice of a product as either the Conex or SuperLink.