Brown dwarfs are the smallest class of star ranging from 13 to 80 times the mass of Jupiter, 0.01-0.08 solar masses; it is thought that they are stars only because fusion reactions involving hydrogen's heavy isotopes, deuterium and tritium, are possible at much lower temperatures and pressures than the proton-proton fusion of their heavier cousins the Red dwarfs. Brown Dwarfs are consequently thought to be quite short lived, burning through their heavy isotopes in a 100 million years or less before going cold.
Deuterium and Tritium can form through neutron capture but Hydrogen and Deuterium both have small neutron capture cross sections making the event unlikely under what might be considered normal circumstances.
Now the question, could hotter true stars in multi-star systems with low mass dwarf candidates produce enough neutron flux, and capture, to make a noticeable difference to the lifespan of their Brown Dwarf companions?
I'd like answers to take into account the temperature/flux range of known stars and assume a tight orbit similar to that of 51 Pegasi b for the Brown Dwarf candidate.