Can I claim compensation from China Mobile for serious losses caused by SMS delay?

The law does not support it, and there is no clear hard and fast rule on whether SMS arrives in real time; Mobile's network access agreement also has an exemption clause in this respect, so you can't get legal compensation for mobile.

Of course, if you are persistent and have strong opinions, mobile customer service may give you tens to hundreds of symbolic appeasement compensation in order to appease your emotions (note: this is not legal compensation).