I'm using the latest version available from the solus sources. The desktop is KDE. I can browse for a while and then all of a sudden the entire browser disappears.
Brave browser keeps crashing
When I was still using Brave (until about 2 weeks ago), I had the same problem. It wasn't deterministic, it was sporadic, and it only happened about 3-4 sync updates ago. Before that, it was always fine. It was also on Plasma.
I'm currently using Vivaldi and Gnome, so I can't say anything about it and/or test it.
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I'm using Brave since i startet with Solus 3 years ago.
It is still running without any issues here, i am also on Plasma with all updates.
On Solus Budgie. Reporting that Brave has been running a-ok. No crashes or other misbehaviours. 
spp71
I'm having similar issues, but with the latest version of Vivaldi.
Tracked down the bugs and seems a problem with the Chromium codebase.
Brave is also build on top of Chromium, so my wild guess is the root cause is the same.
I suggest downgrading to the previous version, until the Chromium folks figure out whats wrong with the latest versions.
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Vivaldi and I assume other Chromium based browsers do not recommend downgrading between significant versions. So 7.2 -> 7.1 is a no no, it can break the browsers profile for your user.
vivaldi-stable is updated to 7.3.3635.4 for this weeks sync. brave, opera-stable and vivaldi-snapshot also have new versions this sync. Hopefully it fixes your issues.
If not you can try deleting the browsers profile/cache.
WARNING: deleting these folders will delete all browsers settings, bookmarks, history / cache, saved passwords, extensions, extension settings etc so backup if that data is important to you.
For vivaldi-stable:
~/.config/vivaldi/
~/.cache/vivaldi/
For vivaldi-snapshot:
~/.config/vivaldi-snapshot/
~/.cache/vivaldi-snapshot/
For Brave:
~/.config/BraveSoftware/
~/.cache/BraveSoftware/
For opera-stable:
~/.config/opera/
~/.cache/opera/