Free and Starter plan members have messaging limits. These monthly limits are applicable to both the sender and recipient. Meaning that both parties must have available messaging credits to communicate.
Once you have reached your monthly limit, you will receive more credits in 30 days. Please note that credits are not based on calendar months so you will not automatically get more credits on the first of the month, it will be a month from when you used your last credit.
If you wish to have more messaging credits before that, you will need to upgrade to a Pro Page subscription which has unlimited messaging.
Another issue could be that email addresses or links contained in a message will not be sent. You can always contact users by visiting the social links listed on their profile.