You should always use the international number format.
When using national format, smstools3 tells to the service center that the format is international, and the message will not be sent. With national numbers you can use a header
To_TOA: National in the message file, but I think that this is not simple with playsms.
Selection of number format can be automated using the global settings
international_prefixes and
national_prefixes. See the bottom of page
SMS file format for details and samples. Unfortunately, with a quick view it seems that this automation cannot be used or is hard to use in Italy.
Please check your status report files. If the number in the file is in international format, it would be best to use international format in all numbering.