I got a freeze during a single player fleet battles session, had to kill the game with task manager, and found this in the RunLog.txt:

Game Loop Mode: Entering MELEE
Nitrous Error: Swap Chain Present Failure:
(887a0005) The GPU device instance has been suspended. Use GetDeviceRemovedReason to determine the appropriate action.
Device Removed Reason: Device Hung: (887a0006) The GPU will not respond to more commands, most likely because of an invalid command passed by the calling application.
See D:\Users\Owner\Documents\My Games\Star Control/SwapChainPresentFailDump.xml for details

There was no SwapChainPresentFailDump.xml file however.

I'm using an NVidia GeForce GTX 970M with 3G VRAM.  Driver version 416.16.  I just noticed there's a new version, 416.34 that I'll install today.  I rarely see these freezes, though, so I can't tell whether it will reproduce or not.

Update: It happened again with the new driver.  It might have something to do with the Fleet Battles AI, since it's happened twice in a row now using the Crazy Cyborg setting and never happened on the Foolish Cyborg settings.

I can't prove that the problem is gone, but I have played 3 more Fleet Battles, this time on 1.1, and the freeze has not happened again.

After switching to the "opt-in" version of Star Control, and updating to the latest nVidia driver, I haven't had any problems since.   *knocks on wood*

I'm getting this issue (Video Freeze due to swap chain) on a fresh install of 1.31 on Steam, even with the opt-in Language Updates Beta, latest nVidia drivers, etc.  I get this error at any point in the game, though I haven't yet seen it in a dialog scene.  I get it when landing, in combat, or in hyperspace after playing the game for a few minutes.  I've also had it happen in the exact same place multiple times when reloading the game and the latest auto-save immediately after experiencing the issue. The specific error I'm getting from the Error_Thread00.txt file is:

Error:
D:\BuildM_SCO_MainStage\Main_Stage\Apps\StarControl\Source\Main.cpp Line: 1148
Swap Chain Present Failure:
(887a0005) The GPU device instance has been suspended. Use GetDeviceRemovedReason to determine the appropriate action.
Device Removed Reason: Device Hung: (887a0006) The GPU will not respond to more commands, most likely because of an invalid command passed by the calling application.
See C:\Users\richm\Documents\My Games\Star Control/SwapChainPresentFailDump.xml for details

My RunLog.txt looks like:

Star Control RunLog.txt
Build description: v1.31 (CL58397) - FinalRelease - CookAssets=Off - NetworkAPI=Steam - DX11   - OptimizeNitrousLibsForDebug=OFF
User: richm
INISettings:etermineVRAM dedicatedVideoMemory 2007MB dedicatedSystemMemory 0MB sharedSystemMemory 4070MB vendorID 10de deviceID 1401
...
Preparing to enter dialog scene JeffDialogScene
Scene Mode: Entering DIALOG
Game Loop Mode: Entering DIALOG
Scene Mode: Exiting DIALOG
Scene Mode: Entering SPACE
Game Loop Mode: Entering SPACE
Nitrous Error: Swap Chain Present Failure:
(887a0005) The GPU device instance has been suspended. Use GetDeviceRemovedReason to determine the appropriate action.
Device Removed Reason: Device Hung: (887a0006) The GPU will not respond to more commands, most likely because of an invalid command passed by the calling application.

Currently running an NVIDIA GeForce GTX 960 with driver version 419.35