I have this weird issue where if my Jeep sits for more than 48 hrs is won't start. The relay clicks like its trying but it will not turn over. I know you are all thinking, well thats not weird, buy a new battery. The weird part is that I can put a 1.25A BatteryTender on it for 5 minutes and it will turn over like it has a full charge and nothing was ever wrong. This has happened to me multiple times including this morning. And I literally mean 5 minutes and its like the battery was 100% fine.

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2006 CRD - GTB2056 turbo by Dieselguy86, Eco Trans Tune, Lift Pump, Week's, HDS Tstat, Racor Filter, ARP's, OME 790's+Top Plate, JBA 2.5", JBA UCA, Moab's+265/75R16, ARB Bull Bar, 4.10's, TrueTracs

I would start by cleaning all connections right down to the starter and making sure they are tight.

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2014 Chevy Silverado Crew Cab 5.3 Ecotec LTZ Z71 4x4
2012 Ford F-150 XLT EcoBoost 4x4
2007 Chevy Silverado 2500 HD D-Max 4x4
1996 Dodge Ram 1500 4x4 (just about dead)
2006 Jeep Liberty CRD

Try just wiggling the battery connections, it may me the clamping of the charger makes better contact... Also could try hooking it up without plugging the charger in. It sounds like corrosion in connections to me too.

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2005 Liberty Sport CRD
Cleaned MAP sensor, ORM, ELM327 Bluetooth OBDII reader with Torque Pro, USA Spec PA-11CHR iPod adapter (used Aux input for Pandora!)
Awaiting install: EVIC, air cleaner hose, and Saikou Michi Catch Can (like a Provent)

Did you hear about the guy who was hooked on brake fluid?
He swears he can stop any time.