[Marshall V. Daut]

If the ground at the crossmember is questionable, then moist, humid air can create a block to the electrical flow. In rainy weather, the same applies: what works fine one day may be intermittent the next. The incorrect gauge cable could contribute to this random go-no go situation. It's best to check that the cables are correct and the ground is clean so that you can confidently eliminate them from equation and then look elsewhere for the cause of the problem.
Don't rely upon the relatively new battery age (three years) to determine whether it is still good or bad. Batteries made these days don't last worth a darn. Three years in my experience is pushing the expiration date. Have the battery checked to ensure the cells are still good. Taking a re-charge is not always indicative of a healthy battery. It may TAKE the charge, but if a cell is weak or the plates have gone bad, the charge will drop by itself, causing cranking problems. This is especially telling on hot days or when the engine is warm.
If none of the suggestions about the electrical flow pan out, you might be back to questioning the starter, especially considering only new brushes were installed during the "rebuild". Lots of other reasons a starter is intermittent, such as a loose terminal or failing solder joints. Do you have another known good starter or can you borrow one to try?
Marshall