Hey @Vilem_Duha! I think I have good news for you on all fronts.
The default max for open tabs is 5, but you can change it! Head to Cursor Settings > Agents > Max Tab Count and set it to 5, 10, unlimited, or a custom value.
As for tabs being lost on restart – on older versions, only the 3 most recently focused chat tabs are restored when you reopen Cursor. If you upgrade to Cursor 3.0 and turn on "Open chat as editor tabs (under Cursor Settings > General > Layout), that limit goes away, and all your open tabs should persist across restarts!
Let me know if this helps!