New 12V battery was totally dead after 2 days

The Bosch battery is perfectly ok for the Prius. A discharge rate of 150ma is still much to high, but if the battery was fully charged should give you about 12 days of inactivity.
How are you charging the battery when it becomes discharged? Are you just jump starting it? or are you charging it with a battery charger?
If you are using a charger what settings on the charger are you using, and how long are you charging it for?
Is the alarm you are using worked by a separate keyfob or is it operated buy the Prius fob?
Does your car have a button below the steering wheel (in front of your knees), and if so have you tried pressing the button?
Can you check the voltage at the battery with the car in ready mode?
Unfortunately removing the fuses that feed the relay coils doe not help. You must remove the relays themselves as it is the contacts that are fed by the dome fuse. If the contacts have stuck together they act like a switch that is permanently on. Relay contacts can be welded together by the current they carry.
I know the relays are very tight to remove, but gently prizing with a screw driver or similar on either side will ease them out.
I realize this is a lot of questions, but with the answers I may be able to help further.

John (Britprius)

 

I have done a lot of research on your problem, and it appears that the ABS relays have been known to cause this problem. Try removing both. The ABS system is supplied by the dome fuse.

John (Britprius)

 

The Prius system check screen is not very accurate. The button below the steering turns off the alarm.
At a charge rate of 6 amps you will need to charge the battery for at least 9 hours, but check the actual charge rate with your meter as often the charge rate shown on the charger is much more than the actual rate. To work out how long the battery needs to be charged divide the battery capacity (45 ah) by the actual charge rate shown on your meter and add at least 1 hour.
(so charging at 5 amps;- 45 / 5 = 9 +1 = 10 hours)
Have you read the update about the ABS relays in my post #22 ?

John (Britprius)

 

150 mA is your phantom draw? That's pretty high. I read 50's about the acceptable max. I checked my 3rd gen; it was around 16.

 

An additional question: Where are you measuring the voltage, at the battery posts? I ask because I have noticed that the measurement at the jumpstart point in the engine bay and the one directly on the battery varies by ~0.2-0.3 V. For what you are doing with John it doesn't matter which of the two, as long you use the same place for consistency.

One other piece of info in regards to parasitic draw which I don't think has been explicitly stated, you need to wait about 20 min before the car is in its fully quiesced state and if you are at the engine bay at this time you will hear the click of the final relay as it switches off. Measure your current draw at this point, not before. The 20 min countdown starts from when you have closed all doors and set the alarm.

hope this helps.

 

Leave your fob well away, it might be causing the car to stay awake. And go through the remaining fuses, hope hope.