After going through the process to renew your residency permit, it can take months for the card to be issued. Apply before leaving Italy, and make sure you keep the receipt from the post office or police department, confirming that you've applied for the new permesso. With a permesso that expires on the day of your return, and only a week before the expiration of your visa, you may have difficulty at the border.
The IATA (International Air Transport Association) Timatic database, used by airline check-in agents, notes:
Alien residents of Italy holding expired Residence Permits or a copy of an expired Residence Permit are permitted to re-enter Italy, provided also holding a receipt issued by the Italian Post Office or Police Department, confirming new permit has been applied for. Applications for renewal must be made within 60 days of expiring, otherwise immigration could refuse re-entry, even if holding confirmation of application. Holders [of] copies of an expired Residence Permit also require a statement, stating that they are holding a copy…”
This is confirmed by Directive of the Italian Government’s Interior Ministry –
A directive from the Ministero dell’Interno, 5 agosto 2006, N. Prot. 11050/M(8) states that one may leave and return to Italy with an expired Permesso di Soggiorno, as long as one has the receipt (ricevuta):
Lo straniero in possesso del permesso di soggiorno, ancorché scaduto, e della ricevuta di presentazione dell’istanza di rinnovo, ha la facoltà di lasciare il territorio dello Stato e di farvi regolare rientro, alle condizioni più volte reiterate con le circolari del Dipartimento della Pubblica Sicurezza.
In translation: The foreigner who has the residence permit, even though it has expired, and the receipt of the renewal application, has the right to leave the territory of the state and to return, under the conditions stated previously within the Circulars of the Department of Public Affairs Safety.