Does an ethernet coupler degrade signal? ?

A proper coupler would not have this effect on the network.

The short answer is NO.  A coupler does not degrade the signal in any significant way that would cause this type of issue.  If there was a short in the coupler you would notice the entire connection dropping out.    The problem is more likely being caused by a cheap home router and\or unstable internet service.  Obsessing over the coupler will likely be a complete waste of your time in solving this issue.  

The main problem the coupler would have is if it was just poor quality and there was occasionally an open circuit created, probably caused by the cable being moved.  If the open circuit condition occurred you should see a message on your computer about the LAN being disconnected.  On Windows the network icon in the system tray (usually lower right corner) will have a red X over it, and you would likely get a pop up message.  A single cable would be better, but unless you're seeing the network disconnect issue the coupler isn't likely the problem.  In reality a coupler is no different than an Ethernet wall jack. 

It's more likely that the application you're using is timing out.  If the application requires you to login and it runs resident on a server at your company, than it is likely using TCP as the transport protocol.  TCP does an acknowledgement for every information packet sent, you send a packet to the server, the server responds with acknowledgement.  The server sends a packet to you, your computer responds with an acknowledgment.  If the acknowledgments are missed or delayed it can cause the application to time out.  

By the way, the maximum length for an Ethernet cable between two network elements is 100 meters (328 feet).  So from your router to your computer you could have a cable up to 328 feet long.

It's called impedance matching. When you insert a coupler you are naturally losing energy because it will not be exactly matched to the cable impedance. So yes, all other things equal, a single continuous cable would be better.

However, having said that, even those have limits as to how long they can be. You should check online to find out what the Ethernet cable limits might be. I've long forgotten them.