I have seen licenses get close to expiration on some software products.
both products did a reasonable notification (the first was batch scheduler which showed the license period remaining at gui startup, the second was a backup product which notified at an hourly interval as soon as there way 15 or so days left.)
In general responsibility for this seemed to be in accounting and with the person responsible for the product.
And from experience, I'd advise You to get i.e. a one-time license for 30 days which only get's paid when it's needed; most vendors seem to offer such.
yesterday I stood at the edge. Today I'm one step ahead.