Last year I tried to buy tickets for April and they weren't available. So I emailed them and this is the answer I got:
"Due to a slight uncertainty about extensive restoration work being carried out in the rooms of Neuschwanstein (i.e. available capacities), as well as a possible adjustment in prices, online tickets for both Hohenschwangau and Neuschwanstein Castle have only recently been made available until March 31st 2024 (winter season).
The two castle administrations gradually 'release' tickets for later dates/seasons, however only at shorter notice and, of course, depending any given regulations/restrictions. We would therefore kindly ask that you check our website regularly for any updates. We only expect tickets for the summer season (01.04.24 – 15.10.24) to be made available in January 2024 at the earliest (subject to change). Unfortunately, we are unable to notify you or make reservations by email due to the high volume of requests we receive.
Please feel free to contact us should you have any further questions. We look forward to welcoming you to the village of Hohenschwangau, soon."
Curious if anyone knows a bit more about this. I guess I'll have to keep refreshing the site every day until they're up.