We've been around this issue before. Does Mr. Randi have a reasonable basis for giving such "claims" short shrift? You bet he does.
First, the claim is inherently hazardous. It is well-known that human beings can go without food for extended periods of time, and there is nothing supernatural, paranormal or occult about that. Extended periods of starvation, however, are known to be harmful to health, and it is unreasonable to expect a claim to be tested that puts the claimant's health at such risk. Mr. Randi does not test individuals who claim, for example, to be impervious to bullets, and with good reason: such a test would be inherently hazardous to the claimant, regardless of the claimant's sincerity and willingness to be tested.
Second, the claim in question requires an extensive amount of time and is expensive to control. The individual in question must be monitored continually for weeks, if not months.
Which is related to the third point, namely, such claims are rife with fraud. Past tests of such claims have shown a propensity on the part of claimants to sneak food when they thought they were not being observed. These were not a mere mistaken beliefs or honest self-delusions on the part of the claimants; rather, they were deliberate attempts to cheat.
In the absence of a compelling reason, there is no reason to undertake the time and expense needed to test such a claim.