People will roll positions when there is good basis potential. This will give a portfolio manager extra alpha. Whether the contract is trading at contango or backwardation will be a significant consideration.
Some months that will be earlier than the 'average' date, some times later.
In other words, it's pretty much a discretionary decision.
Ive seen brokerage reports proving there will be an extra 20 bps available rolling earlier/later than normal. Thats significant in terms of annual bonus to a manager.
I doubt that this is true for financials. But I believe that the spread between the two front months can be distorted by
-> the structure of the inventory (open interest)
-> the physical market close to delivery
Let us take crude oil which is delivered at Cushing as an example. Usually long only commodity funds need to roll their positions over. This means that it can be a profitable strategy going short prior to rollover and then buy from long funds when rollover date is approaching. Then sell the new front month and wait for the next rollover date.
However, from time to time there is a physical shortage in Cushing, due to pipeline maintenance or other reasons, and professional traders step in and purchase long positions to get delivered. In such a case their can be a magnificent short squeeze, as the shorts are trying to purchase back their positions in order to avoid to get assigned for delivery.