Alkane deprotonation by organolithiums
I would bet activation energy for this sort of reaction is quite high, and since primary and tertiary carbons aren't hugely different in stability the sort of H for Li exchange reaction would be very slow. For nBuLi, the reaction would practically not happen, and for sBuLi and tBuLi intramolecular rearrangement (proton shift) is more likely than reaction with solvent, resulting in nBuLi and iBuLi respectively.

Agreed that elimination and precipitation of LiH will be faster than alkyl exchanges in these solution, though I've never checked an old bottle of tBuLi for any precipitate so this is entirely speculative.

Investigating this would be quite challenging, as loss of base power in practice usually happens from slow exposure to O2 and H2O,which would resolve Li2O and LiOH respectively, also basic precipitates.