Cut them open to verify there is no insect damage.

I know all the plums of mine that get hit by PC turn from green to yellow (a sure sign they will drop). Inside will be a nice worm wiggling around.

You wouldn't be getting 2 inch fruit if they weren't pollinized, the tree is probably "self-thinning" because it has only been in the ground a year and can't handle too much. Be grateful--this is much better than setting too much fruit and having your branches crack and fall off, ripping the bark! And all my plum trees only gave me a couple of fruit the first year after planting, so now I learn to wait to thin the plums.

Carla in Sac

Need to know your location.

I don't consider Shiro to be self pollinating.

It sounds like an immature tree to me, its late for drops due to lack of pollination or curculio. Shiro is a heavy setter so you will soon be having more plums than you need.

Scott

I asked for location because here we had a late hard frost a couple weeks after J. plum petal fall. Some of the plums continued to grow for a while but than dropped off- same with peaches. Never had a hard frost so late in fruit development.