I think it’s not likely that ‘the logs are stuck’, I think it’s more likely that ‘the client or system is busy doing something and nothing is being logged’.
Have a look at the links at Tip: Troubleshooting Client Reponsiveness especially the section about ‘long-running evaluations’. There are some links to Analyses you might activate to see if you have some property in your environment that takes a long time to calculate.
One issue I’ve seen is if you have a long-running property set to evaluate “Every Report”, then the report after an action completes might actually be delayed while the client spends more time evaluating that property. Anything that recurses through ‘descendants’ or calculates hashes of large files or directories are notorious for causing problems like that.
If that doesn’t help, you may need to enable a higher level of debug logging on the client to see what it is doing, or open a Support Ticket so the support team can show you how to collect and analyze that info.