I have my doubts that the "random reboot" is SD card related. I have had my 830 for about 4 months now, and I have never installed a SD card. I have been experiencing random restart events from day 1 of owning this phone. My suspicion so far is that this is related to one of these 3 areas:
1. A wireless connectivity problem.
2. A factory installed program or app.
3. A specific piece of hardware that is common across several models of Windows phones.
I haven't done any formal QA on this problem, but this is what I have noticed when casually observing this problem.
1. I was having this problem right from day 1, before any apps were installed.
2. The restarts are occurring regardless of what I am doing with the phone (angry birds, viewing webpages, using the weather app). The most ironic instance of this auto restart, was when it occurred while I was submitting a survey to MS in which they were asking my opinion on the phone so far. In my survey response, I noted that the phone automatically restarted at random times. I'm not sure if they actually got the note in my survey response, because the phone restarted as I was hitting submit.
3. I have never installed a SD card in the phone.
4. This problem seems to occur more often in certain areas of my home where wireless signal strength (both cellular and wifi) are weaker, in the basement for example. I would also point out that I spend less time using my phone in these areas, but auto restarts seem to happen more often.
Here is one last behavior I have noticed when the phone auto restarts, although I haven't determined it's significance. Maybe someone else will have some insight:
When using IE I have 2 tabs open. I open a new tab and begin browsing and open a link from My Favorites, for example. I view the webpage and return to the home screen by pressing the Windows button. When I open IE again, I see the most recently viewed page and when I look at the tabs I see the other 2 tabs open. 3 tabs in total, all showing the last viewed page on each. This is exactly how you would expect the phone to behave.
Scenario 2 is when the phone auto restarts shortly after opening a new tab and loading the page from My Favorites. If a new tab is opened, a Favorite is selected, the page loads, I view the page for about 15 seconds and then the phone auto restarts. When IE is opened again, the new tab has completely disappeared as if it was never there. The phone is crashing just-as, or just-before it is storing the information about this new tab to memory (and/or possibly while trying to send the data about the new tab over wireless).
I would also note that my previous phone was a Lumia 800 that I had for 3 years, and never had this problem once.