Is it normal for hotels to up the price for promotions?

Is it normal for hotels to up the price for promotions? I received an email this week about a free night if booking 3 consecutive nights, but when I check online, the price without the promotion is considerably lower to when I put in the promotional code with my membership number. The price jumps considerably for the same days and the same room. Having already emailed the hotel concerned I have not received a satisfactory answer, just a routine "Please be informed that the hotel rates are subject to changes daily based on the occupancy level." That is plainly not correct as I can still book the rooms for less each day, albeit I don't receive the 3rd night for free and end up paying more if not using the promotion. The fact is the daily rate jumps up to a higher daily rate using the promotion.

Different booking rules, perhaps? Is one refundable and the other non-refundable?

On looking at the site again, maybe the difference is in advance booking compared to best available rate/ custom stay or bonus choice booking. I was doing advance booking, but after applying the promotional code the price goes up.

Further to this, I did end up booking at the advance rate at cheaper rate per night than advertised, also having entered as promotion with their code, which showed in booking, but not after payment. On contacting the hotel to make sure all was okay I was advised that they would not honour the 3rd night free, but after forwarding them the screenshot they have offered the free night but will not refund the amount paid as it was an advance booking, but they will allow the extra money paid to go towards food and beverages which we have accepted. I would say they had a website problem.