I rather suspect that it is not a matter of if but when there will be a commercial oil/gas find in the Falklands basins. Most of the pieces of the puzzle are there as searches on "Falklands basin oil prospectivity" make obvious:
Falklands oil dream taking flight - Investors Chronicle
Falkland Islands Goverment Department of Mineral Resources - North Falkland Basin, play
What the industry is looking for is an 'easy' field that gets enough basic infrastructure into the area to then go after the more serious stuff. The easy field need not be that large and would ideally be water drive or low GOR gas drive (i.e. flare the associated gas) processed via a floater (probably a semi, maybe a ship-shape) and buoy off-loading to tanker. The only land-side infrastructure would be logistics in nature.
They will typically go through exploration cycles that run in low but rising oil prices. This allows for the lower rig rates and higher availabilities. The lag in availability tends to mean that you can't explore in Falklands in low but falling oil prices, and in high oil price periods the rigs are priced out of the Falklands market.
It is a myth that Falklands oil/gas must necessarily be in very deep water. Whilst the first commercial field may be, it may not be. It just depends on who gets lucky first and where. It is perfectly possible - but logistically & operationally tricky - to develop & operate fields in these sorts of isolated areas. An analogue is the NZ fields.
As the oil/gas price trends upwards then at a certain point the finds will cross the economic threshold and bingo things will start happening.
As I am sure the realists amongst you all know the Argentine driver is always domestic and then trigger the LatAm mood music. Having said that the sheer indoctrination of the Argentines into the "las Malvinas son Argentinas" mindtrack has to be seen to be believed even in otherwise thoughtful intellectuals. I have only known a few Argentines who had bothered to find and think through the real history. This has seeped into the whole of Latin American consciousness in the same way that the Brits tend to assume that they are "better" trained soldiers/sailors/airmen than (say) the US without always taking a hard look at the facts. (Not wanting to be controversial but am trying to find an example that will make the Brits squirm a bit).
On the military side I am sure you all know it is not just a matter of comparing ship or aircraft counts and snap cards factoids. But do not underestimate the professionalism of the Argentine armed forces - like the Brits they are a serious bunch that have been let down by their politicians for a very long time. I hope that all will realise there is more that connects us than that separates us.
The irony is that successful finds in the Falklands will also tend to trigger much more and much better informed equivalent work in the offshore continental shelf areas that are indisputibly Argentine and where there has been very patchy exploration work going back thirty years or more as this article alludes to:
Dispute Shows Argentina?s Lack of Oil Exploration - NYTimes.com
Shell old hands have been through cycles of high cost exploration in Argentine waters which has disillusioned the local onshore folk. I have been told about similar experiences at YPF Repsol .
Hope that helps.