2004 Jeep Grand Cherokee Laredo Interior Fuse Box Labeling Diagram

The so called IOD (ignition off draw) current should normally not be more then 35 mA or 0.035 A. Your 0.3-0.6A is too much. The low current is caused by the different memory functions of PCM, TCM, clock and some other stuff.
Here below follows a procedure which i found on internet to investigate the cause of the exessive draw (they mention 0.025 mA as a max, but the WJ manual calls for 0.035 mA). Eventhough the current draw can deplete the energy of your battery, it should not kill it. The only thing is to recharge as soon as possible an empty battery, otherwise a chemical reaction between the plates and the liquid will damage the plates and reduce the capacity of the battery. Attached a page from the WJ manual with the normal IOD currents from several components :

IGNITION-OFF DRAW TEST
Ignition-Off Draw (IOD) refers to power being drained from the battery with the ignition switch in the Off position. A normal vehicle electrical system will draw from 5 to 25 milliamperes (0.005 - 0.025 ampere) with the ignition switch in the Off position, and all non-ignition controlled circuits in proper working order. The 25 milliamperes are needed to supply Powertrain Control Module (PCM) memory, digital clock memory, and electronically tuned radio memory.

A vehicle that has not been operated for approximately 20 days, may discharge the battery to an inadequate level. When a vehicle will not be used for 20 days or more (stored), remove the IOD fuse from the Power Distribution Center (PDC) This will reduce battery discharging.

Excessive IOD can be caused by:

Electrical items left on
Faulty or improperly adjusted switches
An internally shorted generator
Intermittent shorts in the wiring.
If the IOD is over 25 milliamperes, the problem must be found and corrected before replacing a battery. In most cases, the battery can be charged and returned to service.

DIAGNOSIS
CAUTION: Testing for high-amperage IOD must be performed first to prevent damage to most milliampere meters.

Verify that all electrical accessories are off. Turn off all lamps, remove the ignition key, and close all doors. If the vehicle is equipped with a illuminated entry system or electronically tuned radio, allow the electronic timer function of these systems to automatically shut off (time out) This may take up to three minutes.
Determine that the underhood lamp is operating properly, then disconnect the lamp or remove the bulb.
Disconnect the battery negative cable.
Connect a typical 12-volt test lamp (low-wattage bulb) between the disconnected battery negative cable clamp and the battery negative terminal post. Make sure that the doors remain closed so that the illuminated entry system is not activated. The test lamp may light brightly for up to three minutes, or may not light at all, depending upon the vehicle's electrical equipment. The term "brightly," as used throughout the following tests, implies the brightness of the test lamp will be the same as if it were connected across the battery. The test lamp must be securely clamped to the battery negative cable clamp and the battery negative terminal post. If the continuity between the battery negative terminal post and cable clamp is lost during any part of the IOD test, the electronic timer function will be activated and all tests must be repeated.
After three minutes, the test lamp should turn off or be dimly lit, depending upon the vehicle's electrical equipment. If the test lamp remains brightly lit, do not disconnect it. Remove each fuse or circuit breaker (Refer to Wiring Diagrams for more information) until the test lamp is either off, or dimly lit. This will isolate each circuit and identify the source of the high-amperage IOD. If the test lamp is still brightly lit after disconnecting each fuse and circuit breaker, disconnect the wiring harness from the generator. If the test lamp now turns off or is dimly lit, Refer to Charging System to diagnose the faulty charging system. Do not disconnect the test lamp. After the high-amperage IOD has been corrected, the low-amperage IOD may be checked. It is now safe to install a milliampere meter to check the low-amperage IOD.
With the test lamp still connected securely, clamp a milliampere meter between the battery negative terminal post and the negative cable clamp
CAUTION: Do not open any doors, or turn on any electrical accessories, with the test lamp disconnected or the milliampere meter may be damaged.

Disconnect the test lamp. Observe the milliampere meter. The current draw should not exceed 25 milliamperes (0.025 ampere) If the draw exceeds 25 milliamperes, isolate each circuit by removing the circuit breakers and fuses. The milliampere meter reading will drop when the source of the draw is disconnected. Repair this circuit as required, whether it is a wiring short, incorrect switch adjustment or a component failure.

Source: https://www.jeepgarage.org/threads/power-draw-on-2004-grand-cherokee-limited.33242/

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