Update

I have been researching this further.  There is a possibility that this is related to the new container format in the 5D mark III.  This camera now allows high or low compression .mov files to be created.  In the mark II they were all low compression.  The last batch that I created was high compression.  It is possible that PP is having trouble with these.  It still randomly rejects files and randomly reports some as being off-line, yet the next time I connect they are back on-line.  I created a batch of 10 with low compression and they loaded correctly, but have not tested this with a large batch of real files.  I am also checking with Canon to see what has changed.

If anyone has any further advice or experience I'd be grateful.  In the meantime it seems that the only way I can safely process these files is to run them all through the media encode and convert them to mp4 or something similar.

Further update

I am gradually answering my own question here.  For anyone with a Canon 5D mark III you might be interested.

• First batch of footage shot on 5D mk III set to 1080P high compression.  This caused PP and Media Encode (ME) to crash frequently.  Even footage already loaded came back with an off-line message randomly.
• Test set of footage shot on 5D mk II worked perfectly in the same project.  There are no compression options on the mk II.
• Could not convert original batch with ME so used MPEG Streamclip to convert the batch of 100+.  Conversion worked first time.  Import into PP worked perfectly.
• Shot a test batch of 10 with the mk III in low compression and they all imported with no problems.

This points to an incompatibility between PP/ME and the new 5D mk III low compression format files.  I'll report this as a bug to Adobe.  I have already reported it to Canon.

I heard from Canon that there had been issues such as mine with mark III files on PCs, but not on a Mac.  It seems that they are investigating.  In the meantime my system works by using the non-compressed format in the camera.  Just go to your video file setup and make sure that you choose this version for your 24P file type.  If you use the heavily compressed format you will experience the issues that you described.  I have been editing mark II files since 2008 and have had no problems since the Mercury playback engine was released.  With the low compressions mark III files I have similar performance to the mark II files.  I just use the standard template for a DSLR when creating a new sequence and everything works fine with native files.  I never convert them for editing (other than when forced to do so due to the above problem).

I hope that this helps.