There have been a number of different situations where tribunals have accepted that it has not been reasonably practicable to make a claim to an Employment Tribunal in the time allowed.
Lack of knowledge of rights
Where the employee is not aware that they have a right to make a claim to an employment tribunal it may not be 'reasonably practicable'. The tribunal will also look at what it was reasonable for the employee to find out on the period before time ran out - where they could have taken some advice or taken reasonable steps to find out their rights time may not be extended.
See: Porter v Bandridge Ltd  IRLR 271
Lack of knowledge of the time limit
If the employee knows about the right but not the time limit to make a claim it may not be reasonably practicable to make a claim in time. However the employee will have to explain why they didn't seek advice on the time limit which might be very difficult for them to do.
See: Dedman v British Building & Engineering Appliances Ltd  IRLR 379
Fault of advisers
If the employee seeks advice from a solicitor and a cliam is not presented in time because of the misleading or wrong advice of the solicitors this will not allow time to be extended - it is likely that it was 'reasonably practicable' that a claim could be presented in time.
See: Riley v Tesco Stores Ltd  IRLR 103
If the employee is ill it may not be reasonably practicable to present a complaint within the time allowed. Illness later in the period of time allowed might be more important than illness at the start.
See: Schultz v Esso Petroleum  IRLR 488
There may be a range of other situations in addition to the ones set out above. in any case the tribunal will need to be persuaded that the circumstances made it unreasonably difficult or impossible to make the claim in time.