Never say "I beg to acknowledge" or "I beg to remain", or use any phrase of that sort with beg in it. Beg in such a position can have no meaning. Its common use in this way is presumably to be accounted for by a false analogy with the reasonable use of I beg as a polite introduction to a contradiction, "I beg to differ", or "I beg your leave to differ". There is no reason why one should apologise, however faintly, for acknowledging a letter or remaining an obedient servant. See Commercialese.