There is circumstantial evidence for the 1839 proofs being issued up to the early 1880s because ESC 3249 (1738) is a 3rd young head sixpence with an 1839 reverse. The third young head was introduced in 1880. However, the mint equipment was upgraded in 1882 when the old Boulton & Watt presses were replaced. It's only conjecture, but there may have been a few sets of 1839 proofs issued prior to the refurbishment when the old dies may have become redundant - not being compatible with the new equipment? If so, the number made could possibly equal the number of these anomalous sixpences extant. ESC rates them as R5 (5-10 known), which is feasible.
In terms of the penny, it is therefore likely that 1839 dies were always available. The halfpenny proof die was replaced on at least 2 occasions, with both 39 over 41 & 39 over 43 known.