I am having the same issues. The dataset is not huge but I do have a number of measures becasue I need the model to be dynamic. The model works on the desktop (slow but works), but in the serivce it sometimes works and sometimes crashes. Also, I have noticed that the "spinning wheel" that used to tell me if the system was still calculating, is now gone and so I have no idea when all the calculations are compleded (I assume it vanishes when a model is nearing the resource limit). It's quite frustrating becasue you start to think that the model is stuck and then all of a sudden the data in refreshes.
Is this all becasue we are not signed up to Premium Capacity? Other than major corporations, who can afford Premium Capacity at $4,000/month (or more)??? And then you start looking at Microsoft's pricing model for usage you start to wonder how anyone can really understand what their monthly bill is ever going to be. I call it the "Rube Goldberg Pricing Model". Very frustrating.
I just ran into this problem today. I modified a report that I had previously published. The original report worked completely fine. The longest load time was maybe 5 seconds. In this 2nd itteration of the report, I modified one of the measures to use some more complicated logic. I also removed some measures from the model. The data set (which is a set of excel files) is literally the exact same. I've not added anything. At first it worked just fine. I came back to it today and made 0 changes but somehow now it is saying Visual has exceeded available resources. It makes no sense.