This PROBLEM is likely the cause of a hardware problem HTC has had in years prior. there is a notorious problem with some of the antenna springs weakening and allowing the antenna to slighty dislodge and lose signal. for the One X, i think IT was a bigger problem on earlier phone mode runs than it was on later ones, but I can't specifically recall what i read about it previously.
Go to Settings > About > Phone Identity and check your device serial number.
If it starts with HT24 or HT25, you may have one of the earlier models and be more likely to see this type of problem.
If it's an HT26 or later, than it may be more likely that your issue is rooted in something else.
****check and then get back.****
nb:am having a few HTCOne X from AT&t brought to me with this same prblm...thats why i have noted it.🙂)