Under the Default Software Update Plug-in Policy (DSUP), does the "Reinstallation attempts after task failure" refer to a hard count of number of installation failures or is there a reset timer built in which the policy would try again with the patches that failed to install?
The "Reinstallation attempts after task failure" is a hard count setting done on a per policy basis.
If some patches fail to install for whatever reason, like a missing prerequisite patch for example, then the maximum count will apply to those patches. It's possible that disabling the patch policy, saving it, then re-enabling the policy will reset the count. But as long as the patch policy remains active, the counter will remain in effect as well.