No of mentioned behaviors can be classified as 'issues'. At first it is necessary to explain how recaching is working in JotCache :
1. The recache is possible to start from browser (JotCache Management View -> Recache button -> Recache Control -> Start). This process runs on the web server in many cases under CGI/FastCGI PHP.
2. The recache is also possible to start with (Linux) server cron job. This process runs on the web server in many cases under PHP-CLI.
Both run modes CGI/FastCGI and PHP-CLI have its own PHP settings and limitations (for CGI/FastCGI strong implied also from web server settings).
3. Just on beginning of actual recache run the pages which shall be recached are marked in database table #_jotcache column 'recache' with value '1' and new assignment of such pages is not further possible until given recache run is finished.
That means any repeating request to start recache process during running actual one is REFUSED.
Behavior as described :
the cron based recache - every 3 minutes - very effectively for over a year.
Here is doubt that your site can be full recached during 3 min. because on many web sites are usually recached lower as 10 pages per min. You can follow progress of recaching on JotCache Management View Page in real time when you click on column title 'Created' for ordering the cached pages in the time sequence. If the cron job is started each 3 minutes then most cron jobs ends immediatelly because of running (oldier) recache run.
The pages in question eventually did update 24 hours later.
The new updated content is successfull recached during last recache run which took maybe several hours but not 24 hours. See explaination above.
"Recache run stopped due to unsufficient value of Recache Run Timeout (JotCache component parameter set in Options)."
You started recache from the browser and web server settings prevents to run long web request. Many web servers are set to limit each web request longer as 30 or 60 sec. Because it is limitation of web server you cannot remove this limitation by setting in php.ini or from JotCache options. Ask your host company for explanation/ new settings. But take into account that Recache from browser is suitable only for small limited number of pages see
Recache in JotCache Help 5.x.