A paragraph from the Operational Guidelines on Back to Education Allowance:
If there is a change in means circumstances other than part-time work undertaken by the BTEA recipient during the academic year, then a revised decision may be applied.
This means that the underlying claim (Jobseeker's Allowance) can be reviewed if means change during the year, and that might affect entitlement to BTEA.
In the circumstances outlined above, if the money is used to purchase a home (rather than a rental property), then there would be no means to assess. If the money remained in an account for some time, it could then be treated as savings and assessed accordingly.