IPA: /ˌʌn.rɪˈmɪt.ɪŋ.li/
KK: /ʌnˈrɛmɪtɪŋli/
In a way that does not stop or become less intense; continuously and persistently.
She worked unremittingly on her project until it was finished.
Unremittingly → It is formed from "un-" (meaning not), "remitting" (from Latin "remittere", meaning to send back or relax), and "-ly" (meaning in a manner). The word describes an action that is not relaxed or sent back, indicating a continuous or persistent manner.
Think of 'not relaxing' ('un-') and 'sending back' ('remitting') to remember that 'unremittingly' means doing something continuously without pause.