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Sorry to say that Skype is currently facing an outage world wide which you can see on this page http://heartbeat.skype.com/2015/09/skype_presence_issues.html
This outage is happening on and off so sometimes it seems connecting sometimes its not signing in,Currently Microsoft is working on the issue to fix it as soon as possible.You can also use the above link to check the status because once they had fixed it permanently it will be notified in it.
Is there anything else you like to know? if so please do not hesitate to ask using the reply box below and if you do not need further assistance please rate positively using the options just below this reply box or above this page select the rating and click on submit. If you need any help in the future please use this link to ask for me http://www.justanswer.com/computer/expert-john/
Sir/Ma'am skype seems to be working normal now.Could you please check it and let me know the status.