I just recently enabled Filevault on my 2011 Macbook Pro. As long as I do not run out of battery El Capitan let's me enter my password and log into my computer.
If I run out of battery the password screen is presented after power on and it tells me my password is invalid indefinitely. At first I reluctantly assumed user failure on my part. But this is happening everyday now, each time I must enter my backup security key.
After entering the key sometimes it asks me to assign a new password, which I set to what I believe it was before. Other times it just prompts me to enter my password again as if the screen saver had activated and the password works as intended.
I hope this is clear enough. It's very frustrating. I'm guessing I might have to disable Filevault.
EDIT
I ran a test:
I entered the password several times while the machine was powered up for root privileges and on wake from sleep. No problems
I then let the battery run out and again was presented with the boot up password screen. As usual my password was not accepted so again I used the recovery key, only this time I suspect the data on the drive was corrupted in some way as I could not get past the apple boot logo.
I just erased the drive and reinstalled for now.
Best Answer
I found that the problem was faulty ram after doing hardware diagnostic tests. In order to do this you might need to boot from the Apple "ASD" images. To find the correct one for your machine this website has a list of which ASD relates to each Mac product. http://www.dannydullin.com/apple-service-diagnostic-asd-reference-list/
After you know the "ASD 3S***" number you can then search Google to download the image files and write them to bootable storage as explained in the documentation stored inside the images.
ASD 3S108 iMac (Early 2006 17-inch) iMac (Early 2006 20-inch) MacBook Pro (17-inch) Mac mini (Early 2006) MacBook (13-inch) iMac (Mid 2006 17-inch) iMac (17-inch Late 2006) iMac (17-inch Late 2006 CD) iMac (20-inch Late 2006) iMac (24-inch)
ASD 3S116 MacBook (13-inch Mid 2007) MacBook Pro (15-inch Core 2 Duo) MacBook Pro (17-inch Core 2 Duo) MacBook (Late 2006) MacBook Pro (15-inch 2.4/2.2GHz) MacBook Pro (17-inch 2.4GHz) iMac (24-inch Mid 2007) iMac (20-inch Mid 2007) Mac mini (Mid 2007)
ASD 3S123 iMac (20-inch Early 2008) iMac (24-inch Early 2008) MacBook (13-inch Early 2008) MacBook Pro (15-inch Early 2008) MacBook Pro (17-inch Early 2008) Mac Pro (Early 2008) MacBook (13-inch Late 2007)
ASD 3S132 MacBook Air (Late 2008) MacBook (13-inch, Aluminum, Late 2008) MacBook Pro (15-inch, Late 2008) MacBook (13-inch, Early 2009) MacBook Pro (17-inch, Early 2009) iMac (20-inch, Early 2009) iMac (24-inch, Early 2009) Mac Mini (Early 2009) Mac Pro (Early 2009) iMac (20-inch, Mid 2009) MacBook Air (Mid 2009) MacBook (13-inch, Mid 2009) MacBook Pro (13-inch, Mid 2009) MacBook Pro (17-inch, Mid 2009) MacBook Pro (15-inch, Mid 2009) MacBook Pro (15-inch, 2.5.3GHz, Mid 2009)
ASD 3S138 MacBook (13-inch, Mid 2010) MacBook Pro (13-inch, Mid 2010) MacBook Pro (17-inch, Mid 2010) MacBook Pro (15-inch, Mid 2010) MacBook (13-inch, Late 2009) iMac (21.5-inch, Late 2009) iMac (27-inch, Quad Core, Late 2009) Mac mini (Late 2009)
ASD 3S139 Mac mini (Mid 2010)
ASD 3S140 iMac (21.5-inch, Mid 2010) iMac (27-inch, Mid 2010)
ASD 3S142 MacBook Air (13-inch, Late 2010) MacBook Air (11-inch, Late 2010)
ASD 3S143 Mac Pro (Mid 2010)
ASD 3S144 MacBook Pro (13-inch, Early 2011) MacBook Pro (15-inch, Early 2011) MacBook Pro (17-inch, Early 2011)
ASD 3S145 iMac (27-inch, Mid 2011) iMac (21.5-inch, Mid 2011)
ASD 3S146 MacBook Air (13-inch, Mid 2011) MacBook Air (11-inch, Mid 2011) Mac mini (Mid 2011)
ASD 3S147 iMac (21.5-inch, Late 2011)
ASD 3S148 MacBook Pro (13-inch, Late 2011) MacBook Pro (15-inch, Late 2011) MacBook Pro (17-inch, Late 2011)
ASD 3S150 MacBook Pro (13-inch, Mid 2012) MacBook Pro (15-inch, Mid 2012) MacBook Pro (Retina, Mid 2012) MacBook Air (11-inch, Mid 2012) MacBook Air (13-inch, Mid 2012)
ASD 3S152 iMac (27-inch, Late 2012) iMac (21.5-inch, Late 2012) Mac mini (Late 2012) Mac mini Server (Late 2012) MacBook Pro (Retina, 13-inch, Late 2012)
ASD 3S155 MacBook Pro (Retina, 15-inch, Early 2013) MacBook Pro (Retina, 13-inch, Mid 2012) MacBook Pro (Retina, 13-inch, Early 2013) iMac (21.5-inch, Early 2013) MacBook Pro (13-inch, Mid 2012) MacBook Pro (15-inch, Mid 2012) MacBook Pro (Retina, Mid 2012) MacBook Air (11-inch, Mid 2012) MacBook Air (13-inch, Mid 2012)
ASD 3S156 MacBook Air (11-inch, Mid 2013) MacBook Air (13-inch, Mid 2013)
ASD 3S159 Mac Pro (Late 2013)
ASD 3S162 MacBook Pro (Retina, 13-inch, Late 2013) MacBook Pro (Retina, 15-inch, Late 2013) MacBook Pro (Retina, 13-inch, Mid 2014) MacBook Pro (Retina, 15-inch, Mid 2014)