I created a new Jira API token which works ... but the field where it's entered is blank when I reopen the application where I'm using it.
Welcome to Atlassian community and thank you for your question.
I'm not sure to understand your question. Jira API token when generated from personal account settings is showed only one time and the user should save it in appropriate way.
In which application are you entering the token? You mean an app of marketplace or an external tool? As I can understand, it the token is not saved in the application, it depends to application itself
Regards
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