I bound an 11 kb DNA fragment to a QIAquick column; is it completely lost?
FAQ ID -756

Larger DNA fragments bind more tightly to the QIAquick columns. It is difficult to predict whether a DNA fragment larger than 10 kb can be efficiently recovered, because this depends on base composition as well as fragment size. If the fragment is only a few kb larger than the 10 kb limit, it can be helpful to heat the elution buffer EB to 60°C and let it incubate on the column for a few minutes before centrifuging. However, please note that it will become less likely to recover your sample the larger the fragment size is. As we cannot guarantee recovery of fragments larger than the maximum cutoff size, we do not recommend to purify such fragments using QIAquick Kits.

The QIAEX II Kit can be used to extract DNA fragments up to 50 kb from agarose or polyacrylamide gels.