My theory's natural causes.
They were terrified, traumatised children - the older boy had existing health issues with his teeth - it was an era of high child mortality - their carers probably didn't care very much (& would have surmised that RIII didn't want them to survive to manhood).
This was highly inconvenient for RIII. It would be a propaganda godsend to his assorted enemies if he announced their deaths. It would also destabilise the delicate rapprochement he was building with EW.
Don't forget EW was a tough, pragmatic broad. She survived being left a widow with 2 dc from her first marriage, to a bloke who fought on the wrong side in the Wars of the Roses, & came out married to the King of England! She then seems to have been quite the operator when it came to advancing her unpopular family.
I can see her deciding to play the long game - nothing she could do for her boys, but honestly they were probably safer in the Tower than being paraded around the countryside at the head of a rebellious army, & she'd have hoped to get them abroad if she could. Meanwhile, she could help her dds by coming out of sanctuary & setting them up at court.
The boys die - RIII hushes it up. If he'd survived Bosworth he would have announced their deaths, & the country would have grumbled but accepted it, but he needed it kept quiet whilst he saw off Richmond.
After Bosworth...no one could find the kids. Because they'd been discreetly buried in the Tower staircase, & their attendants were not about to admit that to HVII - they would have been scapegoated for killing them on RIII's orders. Plus his new queen was their sister, & might have wanted to avenge her poor neglected little brothers.
They make up a cock & bull story that RIII moved the boys from their care & they've no idea what happened after that. HVII doesn't really believe that, but he certainly doesn't want then popping up alive, so he says nowt. This accounts for him taking later pretenders like Warbeck & Simnel reasonably seriously - he can't prove they aren't genuine!
I'm sure both RIII & HVII would have happily done away with them given the chance. But RIII couldn't afford the scandal between 1483-5, so had it on his 'to do' list for once everything had settled down, & then HVII couldn't find them because they were already dead & hidden under the stairs when he took the throne...