It's not designed to remember your choice from a previous page and I'm not sure it should be that way. Not every model has every option. So if you choose Diesel L4, it simply might not exist if you browse over to some vehicle that doesn't have that option.
Can you explain a bit why you think the setting should stick?
Well, I noticed that the engine type was missing yesterday (at the time that I posted the above), but it is possible that it may have disappeared earlier from a previous edit. So I'll keep an eye out & let you know if it happens again.