You will have to take a tcpdump in the F5, and check what actually happens.
To check in the tcpdump:
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Who terminates the connection?
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Does the connection closes fully in the client side?
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Does the connection closes fully in the server side?
A common problem related with termination in a TCP connection, is the time wait settings.
I would guess that is that case here, but you need the tcpdump to confirm, with the settings from F5 and back end server.
I saw this in the past with Windows servers, here is the link for Windows:
https://technet.microsoft.com/en-us/library/cc938217.aspx