Apparently, the Rav4 has an undersized battery to begin with and is sensitive to under-voltage problems when starting.
The rav's prior to 2009 have an undersized battery -35. Check the
battery and if weak get a 24F for replacement.
As one user mentioned:
I just ran my tests on our RAV. Interesting! It has a Toyota battery.
The size wasn't readily discernible but it fills the battery box.
Since I bought the car used I don't know if it's the original or not.
Anyway, with the car not having been run since noon yesterday and
overnight temperature at 50F, my analog load tester meter read right
on 12V at 9:30 AM today. While cranking it dropped to 9.5 volts. The
engine cranked over 5-6 times and took less than two seconds to start
at which point it jumped to 14V indicating normal charging. After a
few more starts trying to "use up" some voltage I got it just below 9V
but it was hard to read the drop because the engine started so
quickly. Finally I held the load test on it until the "toaster" glowed
red - about 15 seconds. The tester gauge went to 11V and into the
"weak" region. The next start got the voltage down to 8V. Again it
started instantly and sounded like it cranked normally.
Conclusion: It's very possible that a weak battery would still crank
the engine over fast enough to sound okay while the voltage is
dropping low enough (which I didn't reach) to shut down the
electronics. That says changing the battery may be the fix.