When I first moved to Portugal (2 1/2 years ago), I rented an apartment in Lisbon for a month, then Cascais for almost a month. I used Airbnb in Lisbon and VRBO here in Cascais. Of course, things could have changed, but then it was no problem. But it was off season. And, I got great prices.
Since I was curious, I just did a very cursory search on Airbnb. It turned up a number of apartments for a month during the rest of this winter. And, a quick search on VRBO for late spring also gave me a number of choices. Not sure what I’m doing (or not doing) that is giving me different results..