There are two possible reasons. One is dirty contacts, but this should be obvious on visual inspection and are easily fixed up. The other is that an EOS 1N and/or EOS 1V (all variants) will show one bar, or a blinking battery bar, if they have not been used for a considerable time. Remove the battery, then replace it, turn it on and fire the shutter several times at low speed. If the blinking bar persists, an internal fault is indicated and this can be checked at a service bench with a device that plugs into either the hot shoe or the data connection port (hot shoe on the EOS1N, data port on EOS 1V and variants) and runs forced diagnostics on the camera (the diagnostic device powers the camera), reporting back any logged faults, including those starting at the battery). It is this diagnostics run that can also highlight unseen problems with the camera and ideally should be run before the camera is offered to sale. Unfortunately this is rarely done so you really do not know anything about the camera unless it has a clear service report. An EOS 1V can look brand spanking new but still hide faults.
Other report lines include the number of shutter actuations, number of exposures/rolls through camera, shutter speed and aperture variations from tolerance, flash trigger voltage stability, drive readiness, focus speed etc. In all, about 30 tests can be reported on. If the camera is serviced at Canon for whatever reason (not an independant outlet), a test would be made of the camera as a matter of routine.
From my experience, the 2CR5 battery is a lousy choice for powering these cameras (EOS 3, 5, 1, 1N. Fit the power drive booster and 8 lithium AA batteries: speed, reliability, extra vertical shooting comfort and readiness.