I had the same problem (using MS Security Essentials). I 'think' it might have something to do with the AV programs monitoring program activity. It seems like that MS SE 'thinks' a malicious script is running and it stops it.
I tried disabling 'Monitor file and program activity on your computer' in 'Real-time protection' and it seemed to solve the problem.
From there, I did some other testing and found that I could leave the option on and still have successful checkouts by configuring 'Excluded Processes' to include "C:\Program Files\TortoiseSVN\bin\TortoiseProc.exe" "C:\Program Files\TortoiseSVN\bin\TSVNCache.exe"
Either method seems to have worked for me so far. (I've been able to do large check-outs consistently since I've changed the options.) I prefer the 2nd, so that MS SE still monitors for potential malicious activity anyway.