@Dave107You are really guessing about the motivations of the host; and so keep in mind potential assumption flaws if/when you ask for a discount.
-If a host is new to AirBNB, and committed to short-term stays, then even a host with no reviews will likely say "no" to a month long stay. A long term guest delays their ability to have 5-10 groups of people come and go, review the property, and get their reputation rolling.
-New hosts generally already have lower prices, hoping to attract those willing to stay at an unreviewed property. So asking for a further discount could be too much.
-Hosts who are open to discounts for longer stays can already pre-set a "monthly" discount. Look for these people.
-Don't assume that just because the calendar is "open" the host isn't using the home. Don't assume that just because the calendar is open the host is desperate for money, or the home will go to waste. All of these assumptions are often untrue.
-As many, many experienced hosts have noted, aggressive negotiation is usually flagged by experienced hosts as a "red flag" guest (unable to be pleased) and most will simply say no and be done with you.
The most succinct advice: pigs get fat, hogs get slaughered.