Is it an eggcorn, or just a garden-variety malapropism? This one is on the boundary, since there is a one-feature difference in pronunciation. I also have to admit, it's sensible enough to be literally "beseeched by questions" -- if you allow that the questions rather than the questioners are doing the beseeching -- so except for the fact that "beseeched by questions" is obviously a misconstrual of "besieged by questions", it would be fine.
Perhaps surprisingly, "beseeched by questions" has only three ghits (and two of them are reprints of the same article, and the third , though "besieged by questions" has 772.
Posted by Mark Liberman at March 9, 2004 10:43 PM