My automatic updates for MS Security Essentials are working again thanks to WindowsXP-KB2584577-v0.4-x86-ENU.exe from blackwingcat. All I had to do was download WindowsXP-KB2584577-v0.4-x86-ENU.exe from http://blog.livedoor.jp/blackwingcat/archives/1706829.html and run it.
The solutions from Bersaglio and heinoganda work well for people who prefer to update MSE definitions manually, but blackwingcat's solution is the only one I found that got my definition updates to work again automatically. For several years, my definitions have been updated automatically every night. Task schedule wakes my computer from sleep state in the wee hours, which runs a script to do automatic updates, then puts the computer to sleep again. The MSE signature update section of the script is below -
REM Begin SigUp subroutine
:SigUp
REM Enable Automatic updates, wuauserv, so MSE can update definitions.
REM Change wuauserv from disabled to auto.
sc config wuauserv start= auto
REM The following command starts the automatic updates service
sc start wuauserv
REM Automatic updates should now be running.
REM Run MSSE sig update
"c:\Program Files\Microsoft Security Client\MpCmdRun.exe" -SignatureUpdate
REM Update complete, turn off Automatic updates to lessen computer burden
sc stop wuauserv
REM Disable Automatic Updates
sc config wuauserv start= disabled
REM Automatic updates should now be disabled
REM Background Intelligent Transfer Svcs BITS is enabled by Automatic
REM Updates, wuauserv, IF wuauserv runs more than a minute or 2, or,
REM if an update is actually performed. Stop and disable BITS.
sc stop BITS
sc config BITS start= disabled
goto :EOF
REM End SigUp subroutine
My system is XP-SP3. The MSE version is 4.4.304.0. It was about April 19 when I first noticed the automatic definition updates were failing. Just before I installed blackwingcat's solution, I tested MSE automatic definitions update again and it failed again with ERROR: Signature Update failed with hr=0x800700C1. A few minutes later, after applying blackwingcat's solution, I tested MSE automatic definitions update again, and this time the definitions update worked. The fix from blackwingcat is what got the auto updates working again. That was the only change, so that was what fixed it. Thanks to everyone who helped with this, especially blackwingcat.