If I've understood the OP's position correctly
- you have a season ticket
- it's on Southern
- it's a straightforward A-B journey
- off-peak, the service is one train an hour
- you need to make this journey up to three or four times a day to drop off documents and so on
- on completing the A-B journey, you immediately go straight back again (i.e. B-A)
- before leaving for the station, you often check whether the train is delayed, using National Rail Enquiries
- if the train you were planning to get is cancelled or delayed, you leave the office in time for another train which may not be the one straight after the train you were first aiming for
- if the train you were planning to get was cancelled, sometimes you don't travel
There's two angles to this which I think you should bear in mind
1) Look at it from the railway's point of view: the railway basically caters for two sorts of passenger - commuters, who go from home to work, stay there all day and then go home again, and casual travellers, who go somewhere for a reason, stay there for that reason, and then go home again. The pattern you've told us about is rather different: at the most extreme, you could be going from home (A) to work (B), then B-A-B with essentially no pause at A up to four times a day. There's nothing wrong with doing this on a season ticket, but it is unusual. When you are then claiming for delay repay on A-B and B-A journeys at varying times in the day, this is even more unusual - and will cost the railway money.
So someone is doing something unusual that will extract money from the railway. From the railway's point of view, this is what an attempt to defraud the railway would look like. Please note that I am
not accusing you of fraud: I am just drawing your attention to what it might look like to the railway.
As people have pointed out, the onus is on the railway to prove that you are trying to defraud them, and not for you to prove your innocence. But in practice, it will save you a lot of hassle if you give the railway further information to demonstrate why you have such an unusual journey pattern. As various people have suggested upthread, this could well take the form of a letter from your employer, confirming that your duties involve taking papers from one location to another, and confirming (what I infer to be the case) that one of the locations is very close to the station, thus explaining your need to travel B-A and then back again on the next A-B train.
2) Look at the precise wording of the delay repay rules: I see that the GTR (the group which includes Southern) Passenger's Charter includes the following
15.5 Compensation Under our Delay Repay scheme, if your journey is delayed by 15 minutes or more, irrespective of what caused the delay, you’re entitled to claim compensation. Delay Repay is based on the time you should have arrived at your final destination station, not the delay to any particular train. For example, if you’re late because a train is delayed en route we will pay compensation based on the time you arrive at your destination station. We need to know the time of the train you took following a cancelled service if you are delayed due to a cancellation.
The last sentence is the important bit. You need to have made the journey (and this is also implicit in the first sentence). So if you have been claiming delay repay for journeys which you intended to make but actually chose not to, Southern are right to refuse Delay Repay for those occasions. You've already found that they are (to say the least) looking closely at your claims. It would be sensible not to make claims that don't meet the letter of the rules as that will only encourage Southern to look more closely. I'd also suggest that if you are expecting Southern to abide by the letter of the Delay Repay scheme then it's only fair that you also abide by the letter of the scheme.