Players that are suffering a lot of disconnections may be suffering that their ISP, firewall or router is disrupting traffic on port 26000 which is used to connect to the EVE server.
If this is the cause of your problems you can change the port to 3724 to see if that helps.

We recommend this port only be used if you are not able to connect to port 26000. Since this is not the official EVE port, support for connection issues will be limited.

In order to use port 3724, it will be necessary to edit your Prefs.ini file. 

For this, you need to locate the following folder, assuming that you have installed EVE in the default location C:\Program Files\CCP\EVE : ( is C:\Program Files (x86)\CCP\EVE on 64bit versions of Windows )

Press Windows Key + R and paste the following line into the Run window.

Windows XP: %USERPROFILE%\Local Settings\Application Data\CCP\EVE\c_program_files_ccp_eve_tranquility
Windows XP Steam: %USERPROFILE%\Local SettingsLocal Settings\ApplicationData\CCP\EVE\c_program_files_steam_steamapps_common_eve_online_tranquility
Windows Vista: %LOCALAPPDATA%\CCP\EVE\c_program_files_ccp_eve_tranquility
Windows Vista Steam: %LOCALAPPDATA%\CCP\EVE\c_program_files_steam_steamapps_common_eve_online_tranquility
Windows Vista 64bit: %LOCALAPPDATA%\CCP\EVE\c_program_files_(x86)_ccp_eve_tranquility
Windows Vista 64bit Steam: %LOCALAPPDATA%\CCP\EVE\c_program_files_(x86)_steam_steamapps_common_eve_online_tranquility

/Users/username/Library/Preferences/Eve Online/Preferences/p_drive/Local Settings/Application Data/CCP/EVE/settings/ under Macintosh.

Edit the Prefs.ini file. Please change port=26000 to port=3724. Save the file and start the client again.