My 2002 RAV4 never had any problem. One year ago battery went down when lights were left in the car for long time and needed jump start. Battery is still original, may be is that the battery need to be changed. Thanks for advise in advance.

I think your conclusion is correct--install a new battery.

Those Rav4 batteries are really small. You got a good life out of it. It will take quite a few trip cycles to set all your monitors back to ready status. In some cases, several hundred miles, but rare.
Also, around 70-80K miles, the heaters in the o2 sensors start to get lazy and may be setting pending codes, but you will never see a CEL unless it fails.

I am a mobile mechanic, I carry new batteries in the back of my van to seel to people stuck in parking lots, happens a lot in the winter months, these japanese batteries only last three or four winters, then that it.