Having been on both sides of this a few times recently, I'd suggest putting yourself in the shoes of the seller and think about what's running through their mind. There's generally nothing more to it than holding out to get the best value without losing the bidder that is there.
The EA probably suggested a figure the house might achieve, somewhere slightly above the asking price, which will now be stuck in the sellers' head and anything below that will feel like they're not getting fair value. If they think you're not going anywhere they will keep doing viewings until they find a higher bidder or are convinced they won't get a better offer. Depending on where you are in the country and the price point of the property that could mean weeks or months.
If you want to get the property below the asking price then I'd suggest you contact the EA and tell them you need to move on and they are to revoke your offer Friday of next week if there isn't a decision either way. Even if you do this, you can always ring the EA a couple of weeks afterward and tell them that you probably would still be interested in the property if the seller becomes serious. The EA primarily wants to get the property sold or they get €0 for their efforts, the price is a distant second and makes little difference to what they earn.
If you really just want the property and you think it's probably worth the asking price I'd contact the EA and tell them you're willing to offer the asking price but are withdrawing from the process Friday of next week unless a decision is made. The seller will be happier as they at least got the price the EA suggested, you can be happy it didn't go over the asking (as the majority of properties seem to be at the moment).
In either case you don't want to sound keen, you want to sound frustrated and serious about moving on, hence the 'withdraw my offer in a week' not 'I will withdraw my offer'.
I wouldn't agree with getting a third party to contact the EA and ask for details, all that does is make it look like there's more interest and it will tempt the seller to hold on longer. I also wouldn't just leave it to see what happens, you might miss somewhere else, the seller might decide to take it off the market, another bidder might come along etc. The only exception to this last point is if it's a particularly unusual property (expensive, in a slow area etc) which do tend to stay up for a few months, but I presume the fact you think 3 weeks is a long time this is not the case.
