Why do you need a loyalty program (and FYI, before I spent so much time on Customer Development in 2020-2021 I wasn't a fan of 'em, but I'm warming to them now)?
Let's look at our table from yesterday, what I call the "Average Monthly Grid", showing average twelve-month rebuy rates by recency/frequency combinations.
Read down the "Freq = 7" column.
Once the customer purchases for the seventh time, the customer has a 73.4% chance of buying again in the next year. That customer is "loyal" based on my definition (>= 60% chance of buying again in the next year).
What happens if the customer lapses just two months, to a recency = three months?
Well, the repurchase rate is down to 59.6%.
According to my definition of "loyal" (>= 60% chance of buying again in the next year), the customer is no longer loyal.
I mean, seriously, the customer just bought for a seventh time and already after just two months the customer is in a serious state of decay.
The loyalty program isn't necessary for a month or two ... it's the opposite of the Welcome situation (where marketing is badly needed in months 1-3 after a first purchase). The customer is quite likely to buy within months 1-2 following a seventh purchase. The loyalty program should be designed to reign-back-in the customer who has just fallen out of a state of loyalty.
That's what a loyalty program should do, quite honestly. It should not interfere with normal buying. It should help bring the formerly loyal buyer who lapses a few months back into the fold, because loyal buyers decay, too.