Microsoft's support forums have the information on this problem:
"If your 640 handset is on Windows Phone 8.1 and has an OS version greater than 8.10.15116.125, you will not be able to upgrade to Windows 10 Technical Preview currently."
"I know this news is disappointing. This is a temporary, not permanent, situation. Without going into great technical detail, I will summarize and say that if you are on a build greater than the one noted above and update to Windows 10 Technical Preview, your device would not be able to recover back to Windows Phone 8.1 if you were to encounter any device troubles or decide the Preview wasn't to your liking."
The post adds that Microsoft is "actively reviewing possible alternatives" to solve this situation. It sounds like this problem is similar to the one that was encountered by Lumia 520, 521, 525 and 526 devices a few days ago. That issue, which was related to a bug in the Windows Phone Recovery Tool, has since been resolved.
Source: Microsoft; Thanks to Luke for the tip!