It is a limitation of Windows that each scheduled task has its own password set - even if tasks use the same Windows account for their credentials. Furthermore, some versions of Windows do not synchronize these passwords with their own security database.
This means that when you reset the account password, tasks stop running until you also change the scheduled task passwords individually for tasks that are running under that account.
However, you can run a script to address this and reset all the passwords associated with Windows scheduled tasks in one go: this batch file should do the trick. Using psexec.exe (www.sysinternals.com) would allow you to execute it on any machine while sitting at your own PC.
cd /d "%SystemRoot%\tasks
for %%a in (*.job) do call :ChangePW %%a
SCHTASKS /Change /RP %password% /TN "%TaskName%"