The issue can be related with your login form which may be missing form_key
hidden field. If so just add the below code in the form:
<input name="form_key" type="hidden" value="<?php echo Mage::getSingleton('core/session')->getFormKey() ?>" />
TryDebugging Tips:
Try to add breakpoint at the start of Mage_Customer_AccountController::loginPostAction()
function for further debugging.
Also you can check the redirection status in Network tab of chrome console.