I think I figured it out. There seems to be a bug where if you open the log as it's being written to, Aida64 will stop writing to the log. My guess is an exception occurs from not being allowed to write to the file as it's open in another application.
A temporary workaround is to copy the log file before reading from it. But, this is not a long-term fix because other processes may try to open the file for some reason (for example, backup software).