Hi I use the Machery-Nagel Nucleobond extra Plasmid midiprep kit to purify my plasmids of 35kb- these kits are designed specifically for larger plasmids. Hope this helps!

The Qiagen kit is probably your problem. I would definitely switch to a kit that is made for larger plasmids. While you are waiting for the new kit, you could try heating the elution buffer up to 70*C then add it to your column. Heat the column + buffer at 70*C for 5min, spin down at 50g for 1min then at 11,000g for 1min. Also rerun the elution buffer over your column at least 2 times because a lot of DNA remains on the column after the first elution 

Hi Tyger, try the alkaline lysis method, It is very efficient, fast and cheap for DNA purification of large plasmids.

Try CIM DEAE column with 6 um pore size after the alkaline lysis to isolate pure plasmids. This is especially appropriate for plasmids above 15 kbp. And usually you get higher purities and higher yield compared to classical kits, because it is a chromatographic method of isolation and these columns have good chromatographic selectivity and resolution. Already CIM DEAE columns with 2 um pore size could give you excellent results, see the attached reference.

Article Adsorption behavior of large plasmids on the anion-exchange ...