Prius not switching into EV mode - 12v battery

I have a 14' C, 3 years old, has 63K on it. I use the car for local commercial driving so ~40-55 miles/day 8:30am to about 3PM, it idles a bit too since I'll park for ~10-30 mins between trips w/ the ac on low. I've noticed in the afternoon around noon the car does not like to switch into EV mode unless it's below 22MPH. normally the car will go ev under ~42MPH. I also notice the throttle from a stop light the car will be quicker to turn the engine on then using the EV acceleration. here is a video I took coasting downhill in the afternoon to demonstrate the problem:

later that same day I came home parked the car for 2 hours, then drove to the gym. on the way there and back it seemed the engine was running a lot, even when I was cruising around 10-20MPH the engine stayed on

I sprayed the throttle intake with CRC Twice, didn't make any difference. I also checked the vent under the passenger seat and it's clear.

Does this seem like it's a 12V battery issue? What tool(s) can I buy to use to test the voltage?

 

I've seen it do the the idle & fill the battery bars few times, but mostly infrequently. How do I know if the battery fan is running hard? I use the AC on low or the 2-3 from low. that something I can hear from the hood or rear?

outside temp in the afternoon is around ~75-85° lately . no animals ever.

my MPG in the morning is around ~50-60. In the afternoon it's like ~38-45 so a significant difference even though i'm mostly driving local. I also notice if I'm going around 50-60MPH and I let off the throttle it seems to rev itself up for second? is that normal? could it be transmission issue?

 

Battery charging is normal, it fills up and drains as I use EV power. When I idle the car w/ AC it switches on and off normal.

After looking around more I think it may be the battery cooling fan, I do idle it like 1-1.5 hour/day so it may be dirty. Are there any tutorial vids on how to inspect/clean the battery cooling fan specifc for a C? The tutorials for the lift back look daunting I'm going to blow compressed air into the vents with the car off see if this helps first.

 

What is the replacement frequency or expected lifespan for the 12v battery?

 

Had the 65K done 5/11/17. I had them clean the HV fan. My mechanic was skeptical, said if the fan is not working properly it will throw a code. They cleaned it for $85, said the fan had lots of lint.

The prius is now driving normal and actually feels lot faster now, it gives EV mode all day now, EV motor seems more responsive, engine comes on less. I'm back to getting 60+MPG on local roads like usual

My theory -as the car is driven the battery will increasingly heat up, with the HV fan working only 50-70% effective at some point a portion of the battery or all of it be too warm to use so it runs the engine to force more air. seems why I was only able to activate it at 22MPH or lower.

 

I never use the EV button, just keep it in eco mode and and use the throttle for EV.

it now cycles more quickly through stages, so more EV time