Difference between having bitcoin in my wallet or in a third party like an exchange or an e-wallet Is there any difference or any problem or extra fees for having permanently (1 month, 6 months, etc..) my BTCs instead of having them in a local wallet like Bitcon-Qt or Multibit?
Only the respective trade-offs of trusting another party with your money vs trusting yourself not to lose your data.

When you keep your money on an exchange website or online wallet service, you are not only trusting their good intentions, but also that they stay in business and are running a secure service. A significant number of exchanges and OWS have been compromised or put out of business.

When you keep your money on your own devices, you are trusting yourself not to be hacked, fooled into sending money to a wrong address, and to keep your data safe. The latter requires you to engage in a decent backup policy and to have a basic understanding what you are doing. There have been numerous cases of personal computers being compromised (google for example "AllInVain"), people losing their data to hardware failure without having a backup, or recently, someone just throwing his hard drive worth $7Mio in the garbage.