Thoughts...
# Does it work if you connect directly, bypassing the Powerline stuff? Could it be interference?
# Are there caching settings in VLC (I know they're there somewhere, and network is different to local) that make any difference?
# Does it happen on all channels, or only higher-bitrate ones?
# Is anything else streaming from the Pi at the same time? Do you have a NIC bottleneck rather than a LAN issue?
# (Similar to no.4) Is anything else happening that could be causing issues - IO to the SD card, RAM IO, CPU use? Anything that could slow the Pi down and make it less able to serve the streams?
# Is everything okay if you record the streams (just to make sure the Pi can actually keep up with the signal in the first place)?
# Is it okay if you record a stream and then watch it (or something else) over NFS or SMB at the same time (just wondering about the interference angle - HTSP vs a file protocol - UDP vs TCP)?
# Do you have a different client to test - does it work on a different laptop?
# (Similar to no.8) Does it work in different software, e.g. Kodi?
Not sure they're really hints, but it's where I'd start to look, at least...