You are required to re-enter your library ID for each LINK+ book you wish to request. That is tedious and unnecessary. You are logged in when you make the request, and the system knows your ID, so the website should simply resupply the ID for each next LINK+ book you request. Namely, have the computer do the work, that’s what computers are for.
BPL should refer this issue to the LINK+ people, who should fix it.
A competent programmer at BPL could make the feature work properly even if LINK+ does not cooperate.