You might be wrong in your assumption that they are going somewhere else; they might have personal problems, financial problems, health problems, they may have been buying for someone else eg they may have bought burgers but now the kids have left home.
I taught evening classes for many years and didn't like students dropping out (partly because it meant the college might close my class). If they'd been absent for a couple of weeks I'd ring them. At first I didn't like doing it - I assumed it must have something to do with me, and was afraid they'd tell me I was useless - but it was always because of another reason eg they'd lost their regular babysitter, they'd been ill, then felt embarrassed about coming back in case they held up the rest of the class, they'd got a new job, they were frightened of losing their current job so were working longer hours etc. Now, I know that most of that isn't relevant to your business, but I think it shows that we tend to fear that we have done something wrong when we haven't. The point is that all my students appreciated the call and my concern.
Can you contact these former customers saying "Hi, we haven't heard from you for a while and hope things are going well". An excuse for contacting them could be telling them of a new product or service you've got. By coincidence, I got an email earlier today from a boutique where I used to shop fairly regularly, but then I started working at home and no longer needed to buy new business suits regularly. This is how the email starts:
"Hello,
We haven't seen you for absolutely ages. We've changed; we're sure you've changed; and styles have shifted a lot in the past year or two. So we'd like to invite you back in to see us to update your look with a free consultation.
Since you last came in to Wardrobe, there's been a lot going on. Not only have we continued to discover some of the hottest new designers in Italy such as Aquilano Rimondi, Mantu, and Santoni, we've also launched the exclusive Sfera collection."
The email then goes on to say what's fashionable this season, gives a few fashion tips, and then finally offers a 20% discount to me if I contact them before 20 June".