I lean towards them being still alive - but sickly and relatively incapacitated - hence why Richard couldn't produce them. They couldn't leave. Richard III had already gotten them declared illegitimate through the Titulus Regius. Thus, they weren't eligible for the throne. Additionally, they were seen alive close to Easter 1484 playing in the courtyard(?), months after Buckingham was executed. Additionally, there's a record from July 1484 mentioning children's dinner or something, which seems to refer to the Princes.
My guess - they were stricken by an illness rendering them incapable of frequently leaving the tower. They're still alive when Richard III is killed, and Henry VII has them killed to make himself next in line for the throne.