It may be the starter for one side. They come in different ranges, and it is possible one isn't the right range. Some are specific to one power level only, and won't work properly in other power fittings.
I replaced both my starters (the usual thermo mechanical ones) with the slightly more expensive (initially) electronic ones, of the right pwoer range, and so far, no flickering on startup or running, and only two new tubes in four years. The electronic ones wait until the heaters have warmed up, and the mains frequency reaches a peak, when they fire, creating a larger pulse to light the tubes. They then switch out completely, as the power level is now below the trigger point, preventing flicker. Only haveing to strike the tubes once also prolongs their lives, so more economical in the long run.
Hope that helps