We'd need more information to be able to suggest a solution. Are the messages you are not receiving from particular people, or just random? And if from particular people, what do they have in common?
One common problem is when people have recently moved from an iPhone. What happens is that their friends are still trying to use iMessage rather than SMS to text them, but iMessage only works between iOS devices (because Apple won't release it for anything else). So if that's the problem you need the other person to change their settings so that they use normal SMS for texting to you.
If it's not that, can you post again with as much information as you can?