Your connection is only one part
Live video depends on the path between you and the source, the source server's load, the video bitrate and how much data the player keeps in reserve. A fast speed test cannot guarantee that every one of those pieces is healthy.
Stability often matters more than peak speed
A consistent connection usually feels better than a connection that jumps between very fast and very slow. Wi-Fi congestion, distance from the router and background downloads can all create those swings.
If a stream struggles, try a wired connection or stronger Wi-Fi signal, close large downloads and use another available feed before assuming the entire service is down.