[sinsofsolarempirefan]

Nobody knows exactly what happened to the boys, but why in 1483, with speculation mounting that the Princes had been murdered, did he not produce them? The simple fact is that as long as they were alive, his claim to the throne was extremely dubious. Nevertheless, if he could have produced them, it might have stemmed the died of people defecting to Henry Tudor or dropping their support for Richard.
The simplest and most reasonable assumption is that the Princes were murdered some time in 1483 to secure Richard III’s hold over the throne.
The most charitable plausible scenario is that they died of natural causes... at the same time...

[MrsEmmaPeel]

We can't say for certain what exactly happened to the Princes. We know that legally, Richard was the Protector of the country until Edward V reached majority age. We know that Elizabeth Woodville staged a coup that failed. We do know the boys disappeared. We know that Elizabeth sought sanctuary. We further know that Elizabeth publicly reconciled with Richard. We also know that Richard never produced the boys publicly when there was pressure to do so. It could be that the boys were already dead (at Richard's direct command, or as a consequence of a over zealous follower), or that they were alive, but hidden. It is possible that Richard produced the boys for Elizabeth only, hence Elizabeth's interesting reconciliation. I believe it was Paul Murray Kendall who speculated that the boys (now declared illegitamate) were in the protection of his mother, Duchess of York, Cecily Neville. He has a fanciful theory that the boys escaped to the country, where they were raised and lived to an old age.

There are a lot of fascinating twists and turns in this story. Richard didn't need to move on the boys until they became of age, or not at all, if they were considered illegitimate. Henry VII had more to gain from their removal, as his entire family was considered illegitimate by act of Parliament. And weighing claims to the throne (illegitimate Prince versus illegitimate family), Prince Edward had the better claim.

Don't forget that Henry backdated is reign to the start the Day Before the Battle of Bosworth, so that any who fought for Richard III could be considered traitors, rounded up and executed.