I just googled. surprisingly enough,

most what i found supports the opposite claim:

(I googled for 'stability of same sex relationship'. )
From APA - American psychological Association


"A second stereotype is that the relationships of le*****ians, gay men and bisexual people are unstable. However, despite social hostility toward same-sex relationships, research shows that many le*****ians and gay men form durable relationships.
For example, survey data indicate that between 18% and 28% of gay couples and between 8% and 21% of le*****ian couples have lived together 10 or more years. It is also reasonable to suggest that the stability of same-sex couples might be enhanced if partners from same-sex couples enjoyed the same levels of support and recognition for their relationships as heterosexual couples do, i.e., legal rights and responsibilities associated with marriage."