Nothing about a clip happens on a server: your own phone or laptop draws it, frame by frame, and hands you the file. That makes it free and private, and it means the few things that can stop it are all on the device in your hand.
Make your own is greyed out
Tap it anyway and it says why: This browser can't make clips. Open the album on another device to make one. The reel still plays. The current versions of Safari, Chrome, Edge, and Firefox can all make one; an in-app browser (a link opened inside a messaging or social app) is the usual culprit, so open the page in the real browser instead.
It started, then stopped
Making a clip waits while the tab is in the background (Paused while this tab is in the background. Come back to finish.) and picks up when you come back, so keep it open and in front until it's done. If your device gives up partway, you'll see Your clip didn't finish with Retry: your picks are kept, so the retry starts right where you left off.
Share didn't open anything
Where a browser can't hand this video to a share sheet, Share isn't offered at all and Save leads instead: save the clip, then share it from your camera roll or files. If a tap doesn't open the sheet, the clip maker says what to try: Tap Share once more to open it, or Couldn't open sharing here. Save it instead. Dismissing the sheet on purpose is fine: nothing is lost, and the clip is still there.
I can't find the saved file
On an iPhone, tapping Save opens your phone's own share sheet, which already offers every way to keep it: Save Video (or Save Image) into your camera roll, or Save to Files. On any other device, Save is a plain download into your downloads. Search for the event's name: the file is named after it and ends in -clip.mp4.
Add to event isn't there, or didn't work
Adding a clip needs a paid event (and, for a guest, open uploads), and a guest who adds a lot of clips in one day is asked to wait: You've added a lot of clips today. Try again tomorrow. On an event with review, a guest's clip waits for the host before it shows. See add a clip to the event.
Your picks aren't stored either
Partyreel never keeps a copy of your clip or the picks you made. Save the file once it's done if you want it later; the reel is always there to make another.