Which English shire probably lasted less than a century and was absorbed into another (which still exists) in the 11th century?

Hallamshire was an ancient county that existed in the area around modern-day Sheffield in South Yorkshire. It was probably established in the 9th or 10th century and was eventually absorbed into the larger county of Yorkshire. The name Hallamshire still survives in local place names and institutions. The county was part of the larger kingdom of Mercia before becoming a subdivision under the control of Yorkshire following the Norman Conquest in the 11th century.

https://en.wikipedia.org/wiki/Hallamshire

Interesting, but according to the article you referred to, Hallamshire was still listed as a county in the reign of Henry VIII in the 16th century so is not the answer to this question.

The only one I found absorbed that early is Winchcombeshire, which was merged into Gloucestershire after the earlier shiring of Mercia.

https://en.m.wikipedia.org/wiki/Winchcombeshire

Winchcombeshire seems to have lasted from 1007 to 1017, when it disappeared and most of it was absorbed into Gloucestershire.

The history of Winchcombeshire is no obscure tale of a lost shire: the story of its creation, development and demise is intricately interwoven with the story of the development of England prior to the Norman Conquest and the fabric of government which rules our lives to this day. Winchcombeshire comprised what is now the Cotswold area of Gloucestershire and Worcestershire, and its centre was at Winchcombe. A scribe's tantalising marginal addition to the heading of an early-11th-century charter started Julian Whybra's quest for the history and boundaries of the vanished shire, and his research has uncovered important evidence relating to early organisation of land tenure in one of the most turbulent periods in the history of England, dating from the reconquest of England from the Vikings in the early 10th century, through the monastic reform movement that divided England's rulers in the mid-10th century, to the Danish wars under Aethelred the unready in the early years of the 11th century.

https://boydellandbrewer.com/9780851155005/a-lost-english-county/
"A Lost English County: Winchcombeshire in the Tenth and Eleventh Centuries" by Julian Whybra

An article by local historian Tim Porter, in the Worcester Journal of 3rd February 2005, gave a summary of the county of Winchcombeshire. This is the basis of the information that is presented below ... The Anglo-Saxon period has been very much overlooked since the Norman Conquest became the big event in English history - for a lot of people it is as if nothing happened before then. In fact, it was when England was formed as a nation - 1066 was just a regime change.
It is thought that Winchcombeshire was created in 1007 during the reign of Ethelred the Unready. Frequent Danish incursions into the west of England made strengthening local administration - so improving the efficiency of tax gathering - an urgent priority. As a result, five counties were formed - Winchcombeshire, Gloucestershire, Worcestershire, Warwickshire and Oxfordshire. Four of the counties survive largely unchanged to this day, but Winchcombeshire was done away with in the next big shake-up in 1017 and most of it was absorbed into Gloucestershire.

The original shape of Winchcombeshire, combining the lowlands of the Vale of Evesham and Warwickshire with the uplands of the Cotswolds was based on economic good sense. It was important to have a mixed landscape with low-lying fertile areas for crops and upland areas for livestock. This consideration could also explain the presence of so many rich monasteries in the area, such as Evesham, Winchcombe and Hailes. They are all along the edge of the Cotswold Hills, meaning that they could draw wealth from growing crops and from rearing livestock. Traces of this tradition could still be identified in the practices of some modern farmers, who hold land in both areas for different purposes.

https://www.badseysociety.uk/village-life/winchcombeshire-1007-1017-a-short-lived-county-adjoining-wickhamford-and-badsey