I have tried for several weeks with assistance from d-link to get the dap-1360 to work successfully as a repeater on 802.11n with a d-link dir-655. In my experience, it does not work in this mode.
If one forces both units to work at 802.11g the repeater connects but is still ineffective in bandwidth and range of service.
I say this for the following reasons based on my testing in conjunction with the d-link tech support:
With 802.11n from dir 655 bandwidth downstream is ~20-22 mbs and upstream 3 mbs.
Using 802.11n, the repeater does not maintain a connection and has less than 1 mbs bandwidth.
Forcing both units to 802.11g/b, the units connect but the bandwidth through the repeater downstream is only at best 3 mbps when through the router, bandwidth 20 mbs. Moreover, the signal strength degrades very rapidly and only 30 feet from the repeater is ~20% as strong as through the router in the same range.
A level 3 support (higher level training) helped with the above troubleshooting and he was turning over the information to their engineering dept to confirm and to work towards a fix.
In case, you wonder, both the dir-655 and dap 1360 have the latest firmware. All testing was done using the same laptop.
d-link's marketing material says 802.11n is possible. Even with their help, I don't see this to be the case.