Are there signs of digging around the missing rhizomes? Surely something/someone strong enough to pull up an iris rhizome would have left a paw, (or foot ??) print in disturbed soil.
That's a lot of plants gone! As Dave suggests above, if a critter dug them up to eat the leaves, you'll find at least some of the rhizomes laying around - do a search pattern in circles out from where they were.
If you don't find any errant rhizomes, I'd set up a video camera and record for a night or two, to see what's happening. Guess I'm just a suspicious sort, but I'd suspect human 'gnomes' if you don't find any trace of the plants. Got a neighbor with a 'collector' type of garden? Irises are expensive, worth stealing if you're a monetarily challenged plant addict.
