TheKB wrote right, it sounds like a overheating problem.
Your MB probably have in BIOS setting that powers it down if certain threshold is reached, and better mainboards have log, so you need not install any software but just enter your BIOS and check your log.
If your mainboard does not have logging, than install some heat monitoring software which will write log to disk before your PC powers down.
Then you can copy the file and analyze it, find where is the problem and solve it.
New (bigger) monitor probably is working on higher resolution or have higher refresh rate or both (you did not share any data about old/new monitor resolution with us), and different type of cable also can have some influence, that two probably point in direction of graphic card, which often have almost ridiculously big coolers for a reason. It could easily overheat if cooler is not working properly/not mounted properly/thermal paste is not used or some combination of those, depending on your setup.
Second possibility is not overheating, but too weak power supply. Higher resolution and refresh means more power for GPU needed, and if PSU could not deliver it, it could just power down.
Edit:
E248WFP has 1920 x 1200 native resolution at 75 Hz (non-standard, but I adore it!)
SE2716H has 1920 x 1080 native resolution at 60Hz
Weird, you actually downgraded your resolution slightly and only upgraded size of monitor (better for games, curved and larger).
Having in mind that HDMI is working on low voltage (+5V and typicall current is ~50mA, lower than USB), problem is quite probably not there.
With knowledge of above 2nd possibility is now out of question, that leaves overheating, caused maybe not from new monitor but by environment change. That can mean summer, but also gradual increase of dust in your PC, the reason why notebooks coolers often after year or two need cleaning service.
Checking MB/BIOS log would be helpful.
