Pulling down a lead-acid battery too far can kill it. This can happen the first time you do it, or after several cycles of this abuse over time. A lot of RV batteries that could last 4-8 years or more die in 1-2 years from being discharged too deeply, or being "cooked" while left attached to the wrong type of charger.
That your charger-tender shows the battery to be bad could be a charger-tender issue. A battery pulled down too low has too little resistance for the charger circuitry to handle, so the charger protects itself by refusing to try. Many "booster" systems do the same, though some have a manual over-ride.
Higher-end chargers might be able to get a charge started on a really low battery, some old resonance chargers could do it, but another way to get started is to hook it up in parallel to a charged starting battery, which should be able to handle the high initial load, which might be comparable to spinning a starter motor. Running jumpers from an engine battery being charged by an alternator sometimes also works. This has to be done very carefully, with heavy cables, because it is almost like hooking up a short circuit, you can expect major sparking on the final connection, enough to explode any hydrogen gas that might be venting from either battery.
My experience, however, is that a battery reaching this stage often also has a cell shorted, or has lost a lot of usable plate area, and really should be replaced.