How do I convert an ISO8601 TimeSpan to a C# TimeSpan?

You need to add the Time separator to your string. Try this:

TimeSpan ts = XmlConvert.ToTimeSpan("PT72H");

See the duration specification - http://www.w3.org/TR/xmlschema-2/#duration

3.2.6.1 Lexical representation
The lexical representation for duration is the [ISO 8601] extended format PnYn MnDTnH nMnS, where nY represents the number of years, nM the number of months, nD the number of days, 'T' is the date/time separator, nH the number of hours, nM the number of minutes and nS the number of seconds. The number of seconds can include decimal digits to arbitrary precision.

Edit/Update based on comments

As there was some question as to why the string P2M2W5D would not be considered a valid TimeSpan since W is part of the ISO 8601 standard, I wanted to add this update so that if someone runs across that issue they don't have to read through the comments to get the answer. The issue, both for the original string in question P72H and P2M2W5D is that the string must conform to the W3C XML Schema (see the documentation for XmlConvert.ToTimeSpan). When we look at the W3C XML Schema (link above), it references back to the ISO 8601 standard, and in particular to section 5.5.3.2.1 which gives the reason why W is not a valid character in the XML Schema:

Since weeks have no defined carry-over point (52 or 53), weeks should not be used in these applications

You must have missed something in the standard. The following:

System.Xml.XmlConvert.ToString(TimeSpan.FromHours(12))

gives me the string PT12H. So it seems like the time portion needs to be prefixed with a T. And the following parses correctly:

System.Xml.XmlConvert.ToTimeSpan("PT25H")

(To a TimeSpan that stringifies to 1.01:00:00.)

Please use the following format for System.Xml.XmlConvert.ToTimeSpan("PnYnMnDTnHnMnS").

P - The designator must be placed before date format.

nY - Number of years, ex: 2Y
nM - Number of months ex: 4M
nD - Number of Days ex: 6D

T - The designator that must be placed before the time format

nH - Number of Hours ex: 8H
nM - Number of Minutes ex: 12M
nS - Number of seconds ex: 14S

    System.Xml.XmlConvert.ToTimeSpan("P2Y4M6DT8H14M18S")

Here, the confusion part with Month and Minutes have the same letter to denote, but the designator usage makes them separate to understand easily.