"Minerva being unwilling." This simply means "uninspired." Minerva is the Roman goddess of wisdom and patroness of all the arts, someone you want on your team at all times. If she deserts you on a given day, your work will be uninspired and your excuse will be invita Minerva. Critics might also use this phrase to describe an artist or work of art lacking inspiration. However, this excuse won't cut a lot of slack at the workplace where, like Alfred Alistair Cooke, they believe "A professional is someone who can do his best work when he doesn’t feel like it.”
EDIT: I just realized that I forgot to credit my source. The above is from http://www.alanemrich.com/Class/Class_Practical_Latin.htm.