After performing the trouble shooting guide procedure described here:
the battery lasted much longer than before. It dropped about half a percent per hour in watch mode, after it dropped a lot faster from 100% to about 82% however.
When I went to sleep last night it was at 50%. When I woke up after about 8 hours, it was at 1% and about an hour or so later it turned off.
The night before it only dropped about 3 or 4%. I deliberately did not start any activity on the watch to see how battery percentages would develop and to prevent it from powering off during an activity as it did before.
Before I performed the trouble shooting guide procedure, the watch would also quickly turn off after the battery reached about 50%, most of the time during an activity.
What is also strange is that the clock time was about 1 hour and 7 minutes late this morning! I will perform the trouble shooting guide once again, hoping that this will also solve this issue.