I suspect that the answer is that it was just a clerical error, in the sense that no-one cancelled a pre-existing registration for your grandmother.
The wartime arrangements for maintaining the registers of voters (even though there were no actual parliamentary elections prior to the July 1945 general election) were quite complicated and were governed by lots of temporary legislation. Although I can't find an extant copy of it, it appears that the Parliamentary Electors (War-Time Regulations) Act 1943 required that the registers of voters were to be compiled based on the 1939 National Register (the same one that was used for National Identity Cards etc and that we as family historians use today). The
Representation of the People Act 1945 set out that the timetable for compiling the registers was to revert to the pre-war May and October half-yearly qualifying dates, but this system was only intended to come into force once the 1939 National Registration Act had been repealed. I might add, the ROPA 1945 is exceptionally difficult to follow.
Add to that the general disruption and displacement of people due to the bombing and civilian war service, and it is no wonder that the registers may have been somewhat out of date. The main aim of holding the 1945 election was to return the country to a proper democratic basis as soon as possible, and of the resulting Labour landslide victory is seen as evidence of the popular desire to return to normality. It wasn't until the 1948 ROPA that the whole system was given a thorough overhaul.