Just ran the sycon DPC Latency Checker. Latency seems to be hovering around 1030 micro sec with an absolute max of about 1400 micro sec in the DPC Latency Checker.

I also attempted to record to the external hard drive I mentioned earlier. As I said, it's a usb 2.0 drive. I only have one usb 2.0 port on my computer, so I used a usb 2.0 four port hub to connect both the Focusrite 18i20 and the external drive to that port. This failed to resolve the dropout problem.

Some wistful ponderings:
 
I use a UA-4FX for my lappy and it is finicky.  But I believe your specs are reasonable.  Albeit, 7200 internal HD is about mandatory, iirc.  SSD is better.
 
1) Experiment with the ASIO buffers as most may not work.
2) Make sure your USB card has all its switches correctly positioned.
3) Make sure your USB card uses external power if required (albeit some cards operate reasonably with USB-3's power (900mA, iirc))
 
My current lappy (Dell XPS 15) only works with 1 ASIO setting.  Sometimes I have to reset things to that specific setting.
 

See!  both of what I said originally, Jim backed me up too on the "Laptops are problematic" theme. 
 
Until you test for DPCLAT your working blind. your reading is not good at all, My old 2004 Toshiba laptop runs a 50ms, My wife's Lenovo about the same. 300ms is about as High as I would ever want happening. Now you need to figure out what it is that is hogging your resources. Did you try the battery management? 
The Scarlet Mix control should be fine at 10. Even on half the computer you have. 
 

I believe I've got battery management disabled, but maybe there's something I'm missing. I'm set to the high performance power plan for windows 8, with all plan settings changed to 'never'. Is there something further I need to do?

Jim Roseberry
Off-the-shelf laptops are often problematic when used as a DAW.
Let me explain why (it's pretty logical when you break it down).
 
A typical laptop is designed for the "general purpose" end user.
That user is surfing the Internet, using Facebook, sending Email, running Office applications, maybe light photo editing, listening to MP3s, etc.  None of these tasks are particularly taxing.  The general-purpose user is much more concerned about battery-life than how well the machine sustains heavy loads in timing critical applications.
 
When you're dealing with ultra-tight space (small form-factor machines - which a laptop is an extreme example), performance compromises *have* to be made to keep temperature in check.
Notice that clock-speeds of mobile CPUs haven't gone up much the past ~5 years.
Power-management and CPU throttling help keep temps in check.
 
 
Off-the-shelf laptops often use motherboards where the majority of BIOS parameters have been blocked.  
This is done to keep tech-support issues to a minimum.
The general-purpose user will never notice DPC Latency spikes... or a 2ms hiccup in data flow.
When running ultra low-latency audio, those settings can make a huge difference.  
If there's a 2ms hiccup in data flow and your ASIO buffer size is 1.5ms, you're going to experience a drop-out.
There's not much you can do in this case.  The BIOS parameters you need aren't exposed.
 
All that said, some laptops are certainly better than others.
Custom built laptops tend to fair a lot better... as you at least have some control over the components used... and additional BIOS parameters are available.  Even with the best laptops, you're making performance compromise compared to a fast tower.
 
To summarize:
To effectively work at ultra low-latency, your machine needs to be able to (indefinitely) sustain heavy loads (processing and disk) without hiccups.
Those requirements are exactly the opposite of a general-purpose user.
 

Great explanation. Do you have any idea whether running a MacBook Pro with Boot Camp would perform better that an off-the-shelf Windows laptop of comparable cost?

Superpar
I also attempted to record to the external hard drive I mentioned earlier. As I said, it's a usb 2.0 drive. I only have one usb 2.0 port on my computer, so I used a usb 2.0 four port hub to connect both the Focusrite 18i20 and the external drive to that port. This failed to resolve the dropout problem.

This is not surprising. Audio interfaces generally need to be attached directly to a USB port and not a hub. Does the drive work connected to the USB3 port?
 
Does the PC manage recording a single track without dropouts?

I was able to successfully record 16 simultaneous channels of drums both with and without the external drive, with the MixControl ASIO buffer set to 20msec, and the playback and recording buffer sizes in Sonar both set to 1024, and the Dropoutmsec variable set to 1000.
 
In every scenario that I've set up however, both with and without the external drive, the data from my LatencyMon tests consistently point to the USBPORT.SYS driver file (USB 1.1 & 2.0 Port Driver) as the biggest issue, with the highest execution in msec.

So this does not appear to be a dropout issue anymore. By "playback and recording buffers in SONAR" are these the disk buffer settings in Preferences > Audio > Synch and Caching? If so, that is fine.
 
What issue(s) are needing to be addressed?

Yes. The disk buffers in Sonar's Synch and Caching.
I believe the issue needing be addressed is my DPC latency. The Sycon DPC Latency Checker is still reporting latency greater than 1000 microsec, even when Sonar is not in use.