When does the LinkedIn connection limit reset? LinkedIn names no reset day, no hour, and no weekly cycle for invitations. What its help page on invitation restrictions gives instead is a wait: most restrictions lift on their own, and the wait grows with how often you were restricted. LinkedIn will not lift one on request.
How long each wait lasts
It depends on the notice you got, and LinkedIn will not say which kind applies. Its help page sorts the waits into three cases:
a first restriction, the shortest wait, counted in hours
several restrictions in one day, a longer wait, counted in days
too many outstanding invitations, the longest wait LinkedIn names
Tell the planner which notice you saw and its result turns into a pause, with LinkedIn's own wording for that case and the date the source carries.
Limits that do reset on the calendar
Two LinkedIn limits nearby do reset on a set day, which is probably where the idea of a weekly reset comes from. A free account's monthly limit on profile searches resets at the start of each month, and Sales Navigator InMail credits renew monthly too. Both count something other than invitations. The planner shows them with their sources.
A Monday reset, or a week counted from your first invitation, has no LinkedIn page behind it.
What to do while you wait
Stop sending invitations until LinkedIn's wait for your case has passed. Sending one to test it can add a second notice the same day, and with it a longer wait.
Use the time to withdraw invitations that have sat pending for weeks, one at a time. That does not end the restriction, but it clears what LinkedIn names as a cause. When you start again, send fewer than before, spread through the week, to people likely to know you.
If LinkedIn asks you to verify your identity, this is no longer an invitation limit. Stop everything on the account and follow the steps LinkedIn shows.
If you send from Oneprofile, remember its limits keep their own clock and cannot see LinkedIn's restriction. Pause the sequence until LinkedIn's wait has passed. The extension then picks up in your own browser, at the limits you set.