If you do an advanced search (including go via, avoid, etc.) from the front page, then there is no indication in the journey summary at the top-left of the results page that you have advanced options available. This means that if you try and change your search using the box at the top-left of the results page, you can easily forget about the previously selected advanced options.
Example:
1) From the front page, do a search for Cambridge to Peterborough via Stevenage.
2) You get some results.
3) In the search box at the top left of the results page, change the journey to search for Cambridge to Norwich. I don't want to specify a via point for this journey, so don't do anything with advanced options, because none are shown there.
4) This search gives no results, because it's still using the old via point (that wasn't displayed anywhere) and trying to do Cambridge to Norwich via Stevenage.
Clearly if you were only making minor tweaks to the results in the box at the top-left of the results page, it makes sense for the advanced options to be "sticky" and applied to the new search. But if you're making an entirely new search it doesn't make sense. I don't have a sensible UI suggestion for how to fix this, since it's not at all obvious if the user's intention is to tweak their existing search or make a new search. But as a starting suggestion, some sort of warning in that summary box that additional options have been applied to the journey that is shown there, to help avoid making the "Cambridge to Norwich via Stevenage" mistake from my example.