Repetitively discharging below about 10.45v will severely shorten a batteries life (reduce it's capacity to hold a full charge). Also, a discharged battery subject to a freeze (below 32) can be 'killed' immediately (will freeze & swell plates damaging it permanently), and an 'OLD' battery can be killed immediately with a deep discharge.
Good quality battery is designed to 'last' about 1000 or so discharge (to about 20%) /charge (to full) cycles ( or about 3-4 years); but this is substantially shortened if battery 'abused' (discharged below 10.45/20%, overcharged, etc).
Fully charge a NEW battery THEN put a solar cell on to maintain it (keep it topped off) for maximum life (4-5 years!!) ; use charger again if solar fails to keep it at 95%.
Battery condition can be determined with a proper 'battery load tester' (which puts a measured load that matches battery design); a volt-meter alone won't tell you much about the batteries internal condition (ability to hold/provide amp-hours over time).