They were losing on all the fronts, but still italy kept on recruiting new soldiers, and after seeing a photo of Mussolini inspecting an alpine brigade made of 15 years old, I was thinking if he thought that he could win?
By the end of 1944 - but really, since his restoration as head of the so called Repubblica Sociale Italiana in September 1943 - Mussolini's strategic horizon was limited to that of the Nazi Regime. While he retained a modest degree of influence in internal matters due to his sharply declining prestige, the "foreign policy" of Salò was, by and large, that of a puppet state. Whether he wanted to continue or not was immaterial, as his very existence as head of state was predicated on his participation to the Nazi war effort. Under his tenure, the northern regions under German occupation provided a modest industrial output as well as a more relevant contribution in terms of labor force (voluntary or mandatory) which the Nazi leadership and Military commands deemed worth the presence of a significant military occupation corp; while the new Italian military conscripts were employed for the most part in police duties and anti-partisan repression. With few well known exceptions of "historical" units, such as Borghese's X MAS, those Italians who wished for a more direct participation to the German war effort were usually allowed into the SS ranks or tentatively included into mixed units with other residual forces of the Eastern armies.
By then, these weren't really Mussolini's policies or decisions, and worked in good measure independently from him, as the German occupation and police forces had established their own preferential channels to interact with what was left of the Italian bureaucratic apparatus.
Mussolini did make (at first) a few tentative attempts to promote a negotiated peace on the Eastern front - for instance by attempting to recruit the former Italian Ambassador to Moscow as his Foreign Minister - but those were little more than pipe dreams, which accounted neither for the intention of the Allied Powers, nor for the character of the conflict on the Eastern front. At the end of 1944, he had - like many others - begun to wander amidst dreams of "formidable weapons" and improbable reversals of fortune, or to complain about his allies, advisors, military, the people, etc. while displaying a mostly despondent and resigned attitude towards the whole affair.