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If the RA axis is tight, presumably the RA motor would have to work harder in order to move it. Generally though, this should not make a lot of difference if the RA axis is reasonably balanced. When pointing to zenith, perhaps balance might be the problem, hence the RA has to work even harder?
Second point - if the battery is low, and you are essentially running off the battery charger - could the charger be unable to supply the current needed to drive the entire setup? I would connect a multimeter in series to measure the current that is drawn when everything is running. If you are drawing 2 amps and the battery charger is charging at 1 amp, then 1 amp must be coming from the battery which if low, means that the voltage will also be down.
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