I can't say I have had any problems splitting ASF files however I suspect you are correct in assuming that they are not cutting on keyframes correctly as this can cause the effect you describe as well as loss of audio/video synchronisation, video tearing, green blocks and even player crashes.
Most of the commercial splitters are in my opinion a bit of rip-off as they use the Microsoft SDK leading to almost identical functionality, if you have problems with one vendors tool then most likely the same problem will occur with any other. This is why I suggested a shareware tool as you can split your video and then toss the program in the trash.
There is another splitter which I was a little hesitant to mention as it is a command-line utility but I'm sure you'll be able to figure it. ASFBin, free from
Radioactive pages, is the successor of ASFCut and has been written from scratch without using the Windows Media SDK so it should be more error resilient.