Check first http://docs.moodle.org/en/HTML_editor_FAQ
It is pretty hard to guess any particular reason or fix without seeing your site or source - injected code (spam) is easy to find from source but may require cleaning of all php files (or at least config.php), Google analytics scripts usually breaks editor permanently, some custom blocks (javascripts) could explain random appearing/disappearing but if I had to guess it sounds like GoDaddy syndrome...
Can you send some more info about your site - address for example?
I visited your site yesterday with guest access but source looked ok - there were some 3rd party activities, some css errors and some messy MS code , for example local links like
file:///C:\DOCUME~1\kkitchen\LOCALS~1\Temp\msohtmlclip1\01\clip_filelist.xml
file:///C:\DOCUME~1\kkitchen\LOCALS~1\Temp\msohtmlclip1\01\clip_themedata.thmx
file:///C:\DOCUME~1\kkitchen\LOCALS~1\Temp\msohtmlclip1\01\clip_colorschememapping.xml
but I don't think they should break editor. You have obviously just copied and pasted some content from Microsoft products...
One possible reason could be in your browser - some malware or phishing program or some partly functional plugin. Have you tried other browsers elsewhere (in addition to your current browsers) ?
I could not test the editor with guest access but you could try to turn debugging to ALL from site administration and check possible errors. At least normal source did not show any signs of injected code.