LinkedIn's commercial use limit kicks in when you're exceeding normal search activity, which LinkedIn interprets as hiring or prospecting. You'll get a warning as you get closer to the limit.
The commercial use limit resets at midnight PST on the first day of each calendar month. LinkedIn won't lift the limit if you request it. You will never see the exact number of searches still available -- and if you run through your searches too quickly, the warning may not show up.
After you hit the limit, you'll still be able to see search results, but only a very small number.
How to Work Around the LinkedIn Commercial Use Limit
Searching for contacts by name on LinkedIn doesn't count. So, if you're looking for "Jane Doe," typing her name into the search box at the top of every page will have no impact on your usage count.
Browsing your first-degree connections from your connected page doesn't count either.
Finally, you can search for jobs via the jobs page without penalty.
Here's what does count:
Searching for LinkedIn profiles (either on the site or app) using keywords and/or filters.
Clicking on LinkedIn profiles from the People Also Viewed section on the right sidebar.
It's also worth noting browser plug-ins that run searches or view profiles on your behalf might count toward the limit. These third-party tools will search for and view accounts in the background. If you're frequently going over and don't know why, I suggest disabling these apps.
Frequently reaching the commercial use limit is a good sign you should buy Sales Navigator. LinkedIn Premium Essentials and Career plans still include the commercial use limit.