In Microsoft's Emergency Motion for a Stay of Injunction [PDF], it argues that it would be irreparably harmed without a stay, that it's in the public interest to avoid disruption to its business and its partners' businesses, and that while they expect to win on appeal, they'd then be out all the expense of implementing the injunction. However, they already asked the judge in the District Court for a stay on those exact grounds and were denied.
Of course, it's now trying them with the appellate court, so who knows? Perhaps they'll be more amenable, but I'll show you what the judge in the District Court said to those same Microsoft's arguments. In a nutshell, he found irreparable harm to i4i, that without a stay they'd be irreparably harmed in an ongoing way without a way to fix the harm, that it's a small company that was being put out of business by Microsoft's infringement, and that money alone could not fix the problem:

On the other hand, i4i will continue to be irreparably injured absent a stay. As discussed, the evidence shows that Microsoft's presence in the custom XML market has altered the very nature of the marketplace for smaller competitors such as i4i. The fact of Microsoft's infringement causes i4i to suffer irreparable harm for every new XML customer that purchases an infringing Microsoft product. To stay any injunction would only prolong that harm without providing any remedy.

We have his Memorandum Opinion and Order as text now, so you can read it in full easily. While acknowledging burdens to both parties, he weighed them and decided that the burden on i4i without an injunction would be worse than any issue Microsoft faces implementing a change. The only irreparable harm, he decided, was to i4i; the burden on Microsoft, he decided, was something it could absorb. And one thing he wrote indicates he doesn't necessarily believe Microsoft's burden is as great as it claims.

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