Intermittent all circuits busy on international calls

I have a customer using an AsteriskNOW system with Vitelity (US) as their SIP provider. They make a lot of international calls in their office–mostly to Europe, I think. They are complaining about frequently getting an “all circuits busy” message when trying to call overseas. The problem doesn’t seem to be tied to particular phone numbers; a call to a given location may go through at one point in a day and fail later. The dial patterns look something like 011XXXXXXXXXXX, if that helps.

I’ve enabled international calling with Vitelity and removed the restriction for the maximum allowed rate of charge. I’m going to submit a trouble ticket with them, but I’m hoping someone here may have experienced this before. Is it specific to this provider? Is there some configuration to be done with Asterisk that makes international calling more reliable? I know this isn’t a lot of information to provide. I’m honestly not sure where to even start with this problem.

Maybe this belongs in Asterisk Support? I know that cross-posting is frowned upon, but is it acceptable to migrate this topic to a different section of the forum?