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The problem for me is I see nothing wrong when I visit your site – no errors and no problems. I see nothing wrong with your htaccess code. I see nothing wrong with the security log entries you posted – they are not related to whatever is causing the errors.
Troubleshooting BPS is “all or nothing” – either a problem is happening 100% of the time or no problems are occurring. There is no middle ground, BPS does not intermittenly have issues or problems. BPS is designed in a way and the natural nature of htaccess code itself is “all or nothing”. Either it works or it does not – consistently. Not sometimes, not intermittently – all or nothing.
So logically that leaves only 1 possibility. Something else that you either have installed on your website or something that is installed/configured on your server is the root cause of the problem. Example: plugin/theme/server/something else X has a problem intermittently, which is breaking BPS and/or other things on your website intermittently. The root cause of the problem is whatever X is since X is breaking other plugins/themes a,b,c,d,e……. / your website intermittently.
I guess until you figure out what X is, you should not use BPS.
I only have external links to my own websites on the homepage. Are you saying I shouldn’t link out on my blog either?
Install the Firefox Browser, YSlow, Firephp and Firebug or use an online website testing site to check your site load speeds. I see 64 requests when your site loads with at least 15 external links loading on your site.