So it is memory issue. You can compare with Squirrelmail. The way RoundCube handles attachments is rather resource consuming. It is a known issue and devs discuss about it since months.
[15-Jun-2009 01:52:15] PHP Fatal error: Allowed memory size of 16777216 bytes exhausted (tried to allocate 5411979 bytes) in /usr/share/php/Mail/mimePart.php on line 315
[15-Jun-2009 02:27:29] PHP Fatal error: Allowed memory size of 16777216 bytes exhausted (tried to allocate 4842219 bytes) in /usr/share/php/Mail/mimePart.php on line 315
... this indicates that php.ini memory_limit is set to 16M. Increase it to 64M. By default this is done by the .htaccess file in the root folder. You stated yours is missing. So, either download and install it separately or adjust php.ini itself. Notice: .htaccess settings do not apply in cases. Your php may be set to ignore .htaccess files or parts of settings in there.
If you do not have access to your php settings you'll need assistance of your hosting company.