"butterflies for a day" means famous/beautiful/successful for a very short time, like butterflies, which have a very short lifespan, often just a few days.
Example: 'They were a girl band that had one big hit but were just butterflies for a day.'
So 'No butterflies-for-a-day for you' would mean the opposite - said to someone who has or intends to have staying power.
Even in love, you're practical and predictable. No butterflies-for-a-day for you, because you aim for a stable partner with the same background.
As Raymott says, there is not an obvious answer for this. However, here's a possibility.
Apparently some people mistakenly believe that butterflies live for only one day. Perhaps your example is referring to this belief and is saying: "You are not interested in a beautiful but brief love affair, like the beautiful, brief life of a butterfly. You are only interested in finding a partner for a long-term relationship."