When passing through security during one of my trips in April, my OV chipkaart was lost by the security screeners.

My OV chipkaart was laid on the top of my jacket in the box (i had it my trousers' pocket and took it out for the screening), and when selected for secondary and placed in a secondary Xray, it never came out. I immediately alerted the screener that the card is missing, but he just checked my box, said the card wasn't there (duh!), and then told me to "take [my] stuff and leave immediately". I asked him to check the floor near the secondary x-ray, but he refused. I had a plane to catch, so I rushed. Old card cancelled, new card requested. Total damage 11 Euro + 2 days I had to pay for my train tickets out-of-pocket due to inability to use my annual subscription.

Upon recommendation of the Schiphol's social media team, I filed a complaint (and a request for reimbursement) in April. I got an automated reply that I will get a response within 48 hours, and then I got a response that my query requires further research and I will hear from them within a month.

Fast-forward now: Schiphol never got back to me; and their social media team tells me that "due to the nature of [my] claim", they cannot help me.

At the end of the day, 11 Euro is a ridiculous amount, but I was upset by the attitude of the screeners, by the attitude of Schiphol's customer service, and the total lack of interest.

Apart from letting it go, is there something else I can reasonably do?

I'm not sure what else you could do, I think we all know Schiphol security is a mess.
Irrespective of secondary or not, never put anything on top of a jacket, that's a recipe for it getting lost, I always throw whatever is in my pocket under the jacket...

If you have a travel insurance, you can see if they might cover those expenses, though it might not be worth it for the sake of 11€, you could also request a refund from NS for those 2 days.

Yeah, I arrived 2 hrs in advance, spent 1:45 hr in a queue, and then my flight was showing as "boarding" (from a B-gate, no less) by the time it was my turn at the security. Rush...

Good idea about NS, thanks! I didn't know they do so, but apparently they do.

It would seem that "lost" in your OP should be in quotes. A public transport chip card represents value and can be used by anyone anonymously. It's almost like leaving a 20 euro note on top of your stuff. Security screeners should be immune to such temptations but I guess the reality is sometimes painfully different.

Given that OP had an annual subscription on it, it was a personalised ov chipkaart and not an anonymous one...

Yup, exactly. It took me 4 minutes, while we were waiting for offloading some bags, to cancel the old one and request a new one. The old card was useless to anyone who would find it...

This is not new, annoying that it still happens.

According to the media there have been several incidents whereby the security staff of Schiphol has been accused of theft (google: "schiphol security diefstal").

I therefore always put all my belongings into the pockets of my jacket to make it less easy for this to happen.

I doubt theft was an issue here. These cards can only be used by the person who owns it. Also, the fact that the card was on top of other stuff makes it highly likely it simply slid off while going through the xray machine.

Still, the agents should have taken the time to resolve the matter - but having such a lightweight card on top of other stuff is asking for it to be 'wiped off' by the plastic/rubber strands in front of the xray machine.