You mention that you have an external drive connected to a USB3 port.  But what about your audio interface (Roland Studio Capture, according to your sig)?
 
USB 2 devices can be iffy on USB 3 ports (despite their claim of being backward-compatible).  This is why you should always connect a USB 2 interface to a USB 2 port -- unless, of course, you don't have a choice.

The OP said his setup worked fine with X3, seems like his issue lies within Platinum and not his USB ports. I'm having similar issues and the only difference is Platinum vs X3e.

JonD
You mention that you have an external drive connected to a USB3 port.  But what about your audio interface (Roland Studio Capture, according to your sig)?
 
USB 2 devices can be iffy on USB 3 ports (despite their claim of being backward-compatible).  This is why you should always connect a USB 2 interface to a USB 2 port -- unless, of course, you don't have a choice.

The Roland interface is indeed connected to a USB 2.0 port.

pmarangoni
I'm not using any samples at all.  These are jazz recordings with live instruments only.  Not even that many tracks either.  Probably less then 16 tracks and four or five buses.

Have you tried deleting all the plugins in use to see if it changes the behavior. In cases like this a subtractive approach to troubleshooting is useful. My best guess here is that this is a disk streaming issue. Try checking your drive throughput.
Having a different machine to try this on could be useful to compare. Also check if you can replicate this behavior on other projects and compare.
Compare the disk buffer settings in X3 vs Platinum.
 
If you put your files on a share and send me a link we can take a look and see if we can spot anything.

I don't have the luxury of doing any troubleshooting like that. I have just a few hours at most to get the recording done in a remote situation. If Platinum requires more horsepower or specific hardware at a minimum, Cakewalk should indicate these minimum requirements.  Right now, if you go to the System Requirements page, it seems as though my laptop exceeds them by a longshot, yet it's hardly enough.
 
I did try deleting the plugins (most of them, perhaps not all), but it would still stop recording after a few seconds. Only by placing about seven tracks into Archive state was I able to record ONE track.

Noel Borthwick [Cakewalk]
My best guess here is that this is a disk streaming issue. Try checking your drive throughput.
Having a different machine to try this on could be useful to compare. Also check if you can replicate this behavior on other projects and compare.
Compare the disk buffer settings in X3 vs Platinum.
 

Since I'm experiencing a similar issue, how does one check the drive's throughput?
 
Also, why would this happen in Platinum and not X3e?
 
Thanks!

pmarangoni
I don't have the luxury of doing any troubleshooting like that. I have just a few hours at most to get the recording done in a remote situation. If Platinum requires more horsepower or specific hardware at a minimum, Cakewalk should indicate these minimum requirements.  Right now, if you go to the System Requirements page, it seems as though my laptop exceeds them by a longshot, yet it's hardly enough.
 
I did try deleting the plugins (most of them, perhaps not all), but it would still stop recording after a few seconds. Only by placing about seven tracks into Archive state was I able to record ONE track.

Platinum actually uses less "horsepower" than X3. We have several benchmarks to show it.
If you are dropping out on recording you most likely have a systemic problem that happens to show up when recording. How many simultaneous tracks are you trying to record and what audio interface and latency settings are you using? As I said its likely related to your hard disk throughput or perhaps power management.
 
 
You asked if there is something you can do to solve the dropouts. Without some troubleshooting on your end you will never find the source of the problem. You should be able to test this anywhere - I wasn't suggesting troubleshooting on site.
 
Are you sure that you are using identical settings in X3? You can try backing up and copying your aud.ini file from X3 to platinum and see if it solves the problem.
 

The best tool (free!) that I have run across for checking disk throughput is the CrystalDiskMark utility.
 
http://crystalmark.info/software/CrystalDiskMark/index-e.html
 
It is available with an installer or as a portable zip(no installer needed).

abacab
The best tool (free!) that I have run across for checking disk throughput is the CrystalDiskMark utility.
 
http://crystalmark.info/software/CrystalDiskMark/index-e.html
 
It is available with an installer or as a portable zip(no installer needed).

Thank you!

+1 to CrystalDisk utility.
I would get Resplendent Software's Latency Monitor as this may narrow down what is the culprit. It is free.