Reel is designed to be simple and effective, and to leverage the native functionality of ExpressionEngine. To select more than 1 video at a time, we recommend creating a Grid field, and making Reel one of the grid columns. You will be able to select any number of videos this way with less restrictions. You can define the Grid field however you want.
There could be many reasons for this. First we recommend verifying that your API credentials for YouTube and/or Vimeo are correct, and you have not reached any API limits. Unfortunately this verification is not something we can help with. If you're still having issues, open up your browsers developer toolbar and inspect the network requests. Reel makes Ajax requests to the APIs, which you should be able to see the responses for. The responses may contain an error. Reel will display an error in the modal window if it is able to.