Interesting. I never got a warning like that. Mine just crashes usually after a click on the end turn.
Actually I noticed yesterday that the game is unstable in the beginning and then irons itself out and I can play for longer periods. I e, I get three crashes when I first start playing, then on the fourth load it's much more stable.
EDIT: I've come to the realisation that the fog of war might be a contributory factor in these crashes. I've always had some showing when I had the crashes and sometimes I remember seeing a fog of war artefact, a sort of line, forming on the upper part of the screen and then the crash. Don't have any evidence for this though, except what I remember...
Same as this no warnings on my crashes either.
First up I have to say the optimisations between beta 6 and 5 have been huge though I cannot comment hugely about 6.1 because I updated my ram at the weekend but in doing so my video card (old card noticeably not performing to what it should - a Nvidia GTX 680) decided to die and no longer function so instead of a Ram upgrade alone I've got a Graphics Card upgrade as well (Got a cracking deal on a R9 285x). However I've got to say running galciv today was smooth as anything immense galaxy, tight clusters, all AI's occasional on pretty much all settings with all game settings as default. My system is a AMD Fx 8320 running 8 cores at 4.1ghz, 12gb ram and a 2gb R9 285x, which is hardly a high end system (cost me £400 total to build this year - including a 1tb hard drive but no OS, which is less than a console but will kick make them look poor), though it is modern.
Since I've been playing since beta3 I've got to say this game has come along so far and is really looking solid now and even with 4gb ram the optimisations in removing the freezes and crashes have come along miles.