The hardware manufacturing and driver software is written by our client. There is different driver for 32 bit and 64 bit Windows of course.
So on 32 bit Windows, your software talks to one driver, and on 64 bit Windows, it talks to a different one? Let us assume there are new versions of these drivers from time-to-time. So when you only test your software on 32 bit Windows you cannot be sure there won't be some differences in the 64 bit driver which will make the combination of your software + 64 bit driver fail. And from the viewpoint of your users, it does not matter who is to blame (you or the author of the driver), all they see is a non-working system. So even if your code is free of bugs, a test might reveal a bug in the 64 bit driver, and finding such a bug might help you take the right measures (like sending a bug report to the author of the driver).
Of course, when you have used those two drivers for years, and you are very confident that the behaviour is exactly the same, you might skip the tests for one platform, following the arguments in @DavidPerfors's answer. As a compromise, you could run tests on 64 bit Windows only whenever a new driver version is available. Actually, this depends on the complexity of the drivers, your experience with and confidence in them.
Some additional things to consider:
- what OS type is your user base using most? 32 bit or 64 bit Windows? If you decide to test only on one platform, choose the one your users use most often.
- how severe is it when a new release of the software will not work on a less frequently used platform? For example, can your customers immediately step back and install the previous working release? Do they have only some inconvenience or real financial loss by this? If it is the former, testing on only one platform may be fine, if it is the latter, obviously not.