Can aged acetylcholinesterase be reactivated?
Until the late 2010s, it was considered impossible to reactivate acetylcholinesterase that has undergone aging. However, in recent years, new advancements have been made that show promise in this area.
A group of researchers investigated several sulfonium-containing alkylating agents that were supposed to alkylate the phosphonate moiety bound to the serine of aged AChE, in hopes that this would allow the enzyme to be reactivated by traditional methods.

Computational simulations suggested that all three of these compounds would be able to alkylate the aged enzyme.
Another group of researchers studied two aminoalcohols that would act by transferring a proton to the aged adduct. One of the compounds showed promise in reactivating aged AChE, as it was able to do so according to computer simulations. This is the molecule:

What is notable about this aminoalcohol is that it is predicted to be capable of reactivating the enzyme without alkylating the adduct.
Yet another series of compounds was shown to be successful in reversing the aging of acetylcholinesterase. These compounds reverse the aging reaction by alkylating the phosphonate/phosphate-AChE adduct, and also exhibit the potential to reactivate the enzyme entirely.

Unfortunately, they were quite slow to reverse the aging of acetylcholinesterase, with the most active compound, C8, resurrecting 12% of methylphosphonate-aged AChE in one day at a concentration of 4 mM.
In conclusion, while several compounds have shown promise in reactivating acetylcholinesterase that has undergone aging by traditional nerve agents or pesticides, therapeutic methods of administering those compounds have yet to be developed. Furthermore, these compounds have not yet been tested in vivo, under physiological conditions, or against other anticholinesterase agents such as Tabun or the Novichoks.
Sources:
Franjesevic, A. J., Sillart, S. B., Beck, J. M., Vyas, S., Callam, C. S., &amp; Hadad, C. M. (2018). Resurrection and Reactivation of Acetylcholinesterase and Butyrylcholinesterase. Chemistry - A European Journal. doi:10.1002/chem.201805075
Khavrutskii, I. V., &amp; Wallqvist, A. (2017). β-Aminoalcohols as Potential Reactivators of Aged Sarin-/Soman-Inhibited Acetylcholinesterase. ChemistrySelect, 2(5), 1885–1890. doi:10.1002/slct.201601828
Zhuang, Q., Franjesevic, A. J., Corrigan, T. S., Coldren, W. H., Dicken, R., Sillart, S., … Hadad, C. M. (2018). Demonstration of In Vitro Resurrection of Aged Acetylcholinesterase after Exposure to Organophosphorus Chemical Nerve Agents. Journal of Medicinal Chemistry, 61(16), 7034–7042. doi:10.1021/acs.jmedchem.7b01620