What does the connect button do on LinkedIn? It sends the person an invitation, and nothing else changes until they answer. Your button turns to Pending, you are not connected yet, and LinkedIn emails them reminders until they accept or you withdraw it. Once they accept, LinkedIn's help page on connecting says you become 1st-degree connections who can message each other and see more of each other's profiles.
Connecting versus following
Only Connect asks the other person for anything. Follow needs no answer, but it opens no messages either, because LinkedIn lets you message only your connections.
On a profile where Follow is the main button, pressing Connect does both: the invitation goes out, and you start following them at once while you wait for their answer.
How to read the decoder
For a pending invitation, the decoder says not to try again. The invitation already went out, and withdrawing it to send a fresh one stops you inviting that person for a while.
If the button never turned to Pending because LinkedIn asked you something first, pick that symptom instead. A prompt for the person's email address and a question about how you know them are LinkedIn asking before it sends, and each has its own answer. If there was no Connect button at all, why there is no connect button on LinkedIn covers it.
What to do while you wait
Leave the invitation alone. It is already doing the one thing Connect does.
Do not withdraw and resend. It only adds a wait before LinkedIn lets a new invitation through.
Stay in view another way. Reading and answering their posts costs nothing.
Look at the whole pile. LinkedIn names invitations left pending among its reasons to stop an account sending more, and the LinkedIn invitation limit covers clearing out old ones.
In a Oneprofile sequence, a connection request waits too. It learns the answer from your own LinkedIn, in your browser, and the steps after it count from the day they accepted, not the day you pressed Connect.