Well as I said, 5 minutes should be enough to replace most lost charge
[ POST EDIT - see below!! ], but that depends on your alternator, and I'm so used to considering
lost cranking charge as opposed to whatever flattening drain you have - ie, cranking won't flatten the battery anywhere near enough to prevent an immediate off & 2nd & 3rd crank etc whereas your flattening is preventing a crank. (And for lost crank, I usually say 5-10 minutes is enough to replace 90-95% of the cranking charge.)
Now I'd assume the various
experts also checked your charging voltage? It should be 14.2-14.4V, maybe higher after first starting. If it's lower, or if it's lower at idle, recharge takes longer.
And if it's 13.8V or lower, it is not charging the battery properly and it may be a weaker than normal battery. (Greater than
the olde 13.8V 'standard' charging voltage - ie, 14.2-14.4V - is required to
rejuvenate old style batteries (namely to reverse sulfation that occurs with
non-full batteries) and is generally required for newer the technology batteries that incorporate Calcium.
It'd be nice to know your full battery voltage after a good run and after its 'surface charge' has dissipated. It might be 13.5V or higher with surface charge but once that has dissipated it should be ~12.7V (normally 12.67V). A general rule for surface charge is
it may take up to 24 hours to fully dissipate on its own, or maybe a few up to 15 minutes with headlights or hibeams on.
Let's assume you have a 60AH battery and it's 50% discharged - ie, using simple conservative rules = 12.7V fully charged voltage minus 5 x 0.1V = 12.2V. That's using the generally conservative but simple "
0.1V per 10% of battery capacity" rule. In practice it's usually more - maybe 1.3V per 10% - so 50% discharged may be 12.0V; not 12.2V.
Incidentally, whilst deep cycle batteries can be discharged 50%, the recommendation for crankers is no more than 20% discharge - ie, ~12.4V (such voltages being measured Open Circuit aka no load, but 100mA should be close enough to no load).
Assume your alternator supplies 6A for recharge (6A being 10% of 60AH which is a common maximum recharge current specification, tho in practice that is usually exceeded in typical vehicles - at least for 10's of seconds to about a minute after starting).
So 50% of a 60AH battery means we have to replace 30AH which means 5 hours at 6A. Assume ~30% battery inefficiency => ~8 hours (Who's the idiot that reckoned 5 minutes?) Or 5 hours at 8A. Etc.
That seems excessive...
Let's tackle it the other way...
Assume 100mA (instead of 90mA). That's 24 x 0.1 = 2.4AH per day,
Hence 3 x 2.4 = 7.2AH over 3 days. That's 7.2/60 = 12% discharge assuming a 60AH battery.
The
20% recommended limit occurs after (60 x .2 = 12)/.1A = 120 hours = 5 days with a drain of 100mA for a 60AH battery.
The calcs above are VERY rubbery. You may have a different capacity battery and that effects how long you can discharge it (at 90mA or 100mA etc). And if your
xAH battery is weak or old, it may only be 80% of that capacity.
And you may charge at far more than 6A. F.ex my former 40AH AGM cranking battery after minutes of unsuccessful cranking etc would initially recharge at 45A (about 5x more than its specified max recharge current of 20% of AH - ie, 8A) but that would drop to 10A within a minute.
And even if the alternator can spare 100A, the battery may only recharge at 3A. The recharge current is V/R (from Ohm's Law V=IR hence I = V/R) where V is the difference between the charging voltage and battery internal voltage (eg, 14.2V & 12.2V => 2V) and R is the battery's internal resistance that increases with state of discharge, and age (and temperature etc). At best for wet FULL lead acid batteries of ~60AH, R may be 15mR (milli-Ohm) => I = 2V/0.015 = 133A - not that it will be a mere 15mR when 50% discharged, and not that the alternator can supply 133A...
Sorry there's so much of
my thinking aloud above, but it may prove useful.
And it certainly blows my (pathetic) "5 minutes" statement out of the water!
The LVCO (low voltage cut-out, aka battery protector etc) would disconnect the offending load - ie, the alarm.
Though I often recommend the ~$20 MW728 battery protector with 10A switching capacity, I won't in this case because it draws 10mA when merely sitting there monitoring, and more when its relay is switched on. I don't recall its "on" draw, but it is probably in excess of 50mA which is significant compared to your load. IE - if it's 90mA, your battery reserve time is halved (approximately).
The was an AUD$22 kit from Oatley electronics but I think that has been discontinued (Oatley kit K227
12-24V Dual Battery Controller). It has a standby consumption of 50uA, or 500uA with status LED, and uses a latching relay with an 80A contact rating. Hence it's a mere 50uA or 500uA (ie 200 or 20 times less than the OFF MW728) except when changing relay state - ie, off to on or on to off.
There would be low current circuits - maybe using MOSFETs instead of relays - but I'm unsure of commercially supplied units or kits. (Are you keen to DIY build an electronic circuit? Or hack some commercially available offering?)
A key consideration is the hysteresis - ie, LVCOs or battery protectors as with voltage sensing "battery isolators" have a disconnect (load) voltage and a reconnect voltage.
When a load is removed from a battery, the battery self recovers and increases its terminal voltage. You'd probably want the alarm/load to NOT reconnect unless the voltage exceeds (say) 12.6, ie the battery has been reasonably recharged. (I had a circuit for the MW728 to be isolated once it doodie the load off, tho that involved a relay. But the same principle could be used on others, and a MOSFET used instead of a relay.)
FYI - I have written about a long unused but fully charged 40AH AGM (identical to the AGM I mentioned above) that caused "hunting" - the MW728 with cut-in voltage of 12.5V and cut-out of 11.8V when powering a 4A cooler would switch in & out over 30 second cycles. That was due to a "weak" battery and it was solved one the AGM has a 'proper' charge off the alternator - ie, a high current blast that blew away
the cobwebs. Yep, alternators are often better than battery charges (because they can supply heaps of Amps).
And yet again I recall on of my gurus saying "
batteries are more of an art than a science".