It is not likely that a failing battery is causing your problem, but.....GM cars and trucks can be susceptible to having unexplainable electrical symptoms, which disappear after replacing the battery or the alternator. If an internal battery connection starts to fail or the alternator has diodes that are going bad, electrical "noise" can appear on the 12 volt circuits. This noise can then confuse the computerized modules. As time goes on, the processing speed of automotive computers increases, making the modules more sensitive to poor quality 12 volt power.
Even if you solve the problem by removing power to reset, keep in mind that more symptoms (not necessarily identical) can appear in the future.