I am new to OS X. Yesterday I set up my email accounts in Mail. It immediately synchronised my emails from my inbox. However, since then I don't get my mails, although I see them through webmail. I heard Mail in Mavericks had problems with IMAP, so I tried to install Thunderbird and Postbox as well with the same result which means I can see the emails I received before yesterday, but none of the new ones. I even tried rebooting but that did not help either.
What is the problem and how can I solve it?
UPDATE: I do not use gmail, my account is hosted by a private provider.