Lionchief power drop

If you haven't already done so, running additional power connections to the section where you are experiencing the loss of power should help.  Every piece of track you add to your layout adds a voltage drop.  If any track pin connections are loose, that cumulative voltage drop can be enough to experience a loss of power to the Locomotive.  Setting- up on carpet can exacerbate this issue where these connections flex as the locomotive travels over them.  Most experienced model railroaders recommend adding power connections to the track about every 10 feet or 10 sections of track.

To add a power connection would I just use spade connectors underneath the track from one section to another?

That's one way to do it.  Any method that will make out of the way electrical connection(s) should be an improvement.

I have another power supply, could I use the second one on another part of the same track. It is the 18v power supply that connects into the side of the terminal section.

It's better if the additional power drop comes directly from the transformer. Depending on what transformer you have, you should either be able to add a second set of wires to the terminal outputs or split the existing wires into two - one for each power drop.

You could also hook your transformer output wires to a terminal block and then run two sets of wires to your track, but that's a little overkill for a 20' layout.   

No need to use a second power supply.

Definitely don't add another power supply to the same track!  You could potentially damage something(s).

Thanks for the help. I'll try adding a power drop every ten feet or track and see where I get from there.