I can't reproduce this issue.

I also thought at first I can't reproduce it, but had set the refresh time too high:
Logged in on https://demo.sogo.nu/ as "sogo3". There were two emails from "Wolfgang Fritz" in the Inbox. I typed "Fritz" in the search box and got the two results. I then waited for the refresh, with the result that the list cleared and "No message" was displayed.

Using your browser's developer tools, can you inspect the XHR query performed when refreshing the mailbox? You could also check the response and make sure that the headers key contains all the expected messages.

I logged in to https://demo.sogo.nu as sogo3 and set the refresh time to 2min. Here are the requests and responses:

date: Tue, 23 Feb 2021 15:44:25 GMT
request: {"sortingAttributes":{"sort":"arrival","asc":0,"match":"OR"},"filters":[{"searchBy":"subject","searchInput":"Fritz"},{"searchBy":"from","searchInput":"Fritz"}]}
response: {"unseenCount": 2, "threaded": 0, "uids": [2, 1], "headers": [["To", "hasAttachment", "isFlagged", "Subject", "From", "isRead", "Priority", "RelativeDate", "Size", "Flags", "uid", "isAnswered", "isForwarded"], [[{"name": "Wolfgang Fritz", "email": "sogo3@sogo-demo.inverse.ca"}], 0, 0, "\"Persönlicher Kalender\" wurde erstellt", [{"name": "Wolfgang Fritz", "email": "sogo3@sogo-demo.inverse.ca"}], 0, {"level": 3, "name": "Normal"}, "14:27", "2.1 KiB", [], 1, 0, 0], [[{"name": "Wolfgang Fritz", "email": "sogo3@sogo-demo.inverse.ca"}], 0, 0, "\"Persönliches Adressbuch\" wurde erstellt", [{"name": "Wolfgang Fritz", "email": "sogo3@sogo-demo.inverse.ca"}], 0, {"level": 3, "name": "Normal"}, "14:28", "2.1 KiB", [], 2, 0, 0]]}

date: Tue, 23 Feb 2021 15:46:18 GMT
request: {"sortingAttributes":{"sort":"arrival","asc":0,"noHeaders":0,"dry":1},"filters":[{"searchBy":"flags","searchInput":"unseen"}]}
response: {"unseenCount": 1, "threaded": 0, "uids": [1], "headers": [["To", "hasAttachment", "isFlagged", "Subject", "From", "isRead", "Priority", "RelativeDate", "Size", "Flags", "uid", "isAnswered", "isForwarded"], [[{"name": "Wolfgang Fritz", "email": "sogo3@sogo-demo.inverse.ca"}], 0, 0, "\"Persönlicher Kalender\" wurde erstellt", [{"name": "Wolfgang Fritz", "email": "sogo3@sogo-demo.inverse.ca"}], 0, {"level": 3, "name": "Normal"}, "14:27", "2.1 KiB", [], 1, 0, 0]]}

date: Tue, 23 Feb 2021 15:46:25 GMT
request: {"sortingAttributes":{"sort":"arrival","asc":0,"match":"OR"},"filters":[{"searchBy":"subject","searchInput":"Fritz"}]}
response: {"unseenCount": 1, "threaded": 0, "uids": [], "headers": [["To", "hasAttachment", "isFlagged", "Subject", "From", "isRead", "Priority", "RelativeDate", "Size", "Flags", "uid", "isAnswered", "isForwarded"]]}

It is noticeable that a (faulty) update occurs before the actual response.
Hope it helps?!