And here is an article by a former writer, charting its decline over the past decades. The article suggests that Punch was a victim of the rise of television and the decline of satirical magazines. Though you'd think that with the rise of web-based humour, a revitalised heir to Punch might be able to carve out a niche for itself.
(I have fond memories of reading Punch in the school library in the late 80s. The publisher's attempt to go for the youth market was evident; they kept profiling people like Stock-Aitken-Waterman, or going on about which club Patsy Kensit or someone was seen at. All this probably led to the formation of magazines such as Oldie, which eschewed all the yoofist stuff and undoubtedly bled Punch's circulation. Though the pre-shut-down Punch did have the classic cartoon caption contest, something the relaunched one sorely lacked.)