If I'd have to summarize the proposed explanation that unfolds in the lines that follow in a few words, I would say that, the economic reasons behind a high tax rate on repairs are related to the effectiveness of revenue gathering and are also about providing the proper set of incentives to private economic agents.
Governments tax in order to finance spending, according to textbooks. It would seem rather trivial to assume that, like all rational agents that populate textbooks, it, too, pursues its ends in the most efficient way (in a traditional means-ends kind of calculation).
In the case of taxation, it also seems trivial to assume that the government will choose to impose only those taxes that are expected to produce the greater amount of revenue with the least push-back from the economy. It is common ground in neoclassical economics that taxes distort economic outcomes.
Therefore it follows naturally that taxing would be more productive (in terms of raising revenue) when applied on abundant (or relatively abundant-no free lunches, remember?) tax bases. Also, it seems that it would be more probable for a government, to target consumption spending rather than capital expenditures. In that way, it would avoid distorting incentives (by taxing capital income, for example).
Having set the stage thus, what needs to follow is an explanation of how exactly housing repairs and new houses construction fit in the so neatly constructed frame.
When a house owner-or a house tenant, for that matter-need to fix a leaky roof, they forgo a portion of their income-lets assume that it's 'income' and not 'wealth', for the sake of simplicity-for the purchase of repair services and relevant commodities. The amount of money that is extinguished, will provide the government coffers with 20% (as per example) revenue.
Consider now what will happen in the case where there are a lot of leaky roofs. It will come as no surprise that there will be a lot of repairing going on and as a consequence, there will be comparable a lot 20%'s of those expenditures going into the government's coffers.
Therefore, it seems plausible, that when the stock of houses is old and in need of repairs, taxing the amount spent on repairs seems like an effective way to pile up revenue.
On the other hand, the case is a bit different if we assume that instead of many house owners there are some real estate firms that own and distribute housing services in a country or a region.
In this case, under the assumption of "leaky roofs" it is not clear before-hand if it is in their interest to expend a considerable sum of money on repairs. Especially, when spending this much would also be burdened with the excessive tax rate. Perhaps, it is in their interest to build rather than renovate.
When the government chooses to incentivize private agents like that, it seems probable to assume it expects that, the expenditure on new buildings will create such a multiplier effect in the economy, that will-hopefully-overcompensate for the loss of revenue from the other options that got dis-incentivized ('repairs'). Also, opting for building new houses increases the stock of housing in the economy, which is another way of saying that the (residential) capital stock increases.
Therefore, it would appear that, when the government selects a high tax rate on housing repair services-as compared with the tax burden of new buildings-it is effectively 1. demonstrating its urgent need for cash and it is either acknowledging that 2. the residential housing capital stock is in dire need of repairs (derelict capital stock) or that it does not expect 3. the real estate developers to actually invest in new housing that would, in turn, invigorate the economy and create new sources of tax revenue.