changes in output to the oil rigs / refineries themselves can easily be ramped/up and down, the problem is the industry relies on a complex network of "smaller" offshore construction companies[1] which are not so flexible in the sense that they can just stop without repercussions. They supply a range of services such as inspection, pipe-laying, testing and connecting actual well-heads[2] using ROV's and deep-sea saturation divers. Staffing these jobs is highly volatile since most people working for them are also freelancers flown in from all over the world. When they bid for these projects (with Shell, Conoco, and others) it takes weeks/months to mobilize their personal, ships and technology for the job.

Usually when there is a reason to reduce capacity on a rig (mostly due to weather) it's normal to just stand-by (sometimes for weeks) until they can continue with the job. When I worked offshore it was never possible to say when I get back home, e.g. the job was estimated to last 10 days but could end in 4 months. And once we were done we were almost always flown to a new destination (so they would try to keep us out there as long as possible). While places like the North Sea regulations would be strict (28 days offshore would be max before you have to go back to shore), in the Golf of Mexico, or in Asia we would never have such rules. I know people who spent months locked in the compression chambers (sat system) or until the project was over. And none of us dared to say we want to go home (it would be career ending).

[1] Oceaneering, McDermott, ...

[2] https://en.wikipedia.org/wiki/Wellhead