Just traditional over a very long period that lovers' separation more often than not happens to be the customary 'seven long years'. It occurs in several old ballads such as 'Lord Bateman'. It may or may not have something to do with the statutory period of apprenticeship served in most trades. Many apprentices could not afford to marry until their apprenticeship was served. Then we get such phrases as 'The seven-year itch'. There must be some significance in it.

Meanwhile here are some other song numbers just for fun!
10 green bottles
9 times a night
8 shillings a week
7 nights drunk
6 jolly miners
5 foot flirt
4 drunken maidens
3 jolly butchers
2 lovely black eyes
1 man went to mow.