The increase of energetic electromagnetic flux during solar flares and particle precipitation during geomagnetic activity are among the most important sources of neutral density disturbances to the Earth's thermosphere. However, disentangling the role of X and EUV radiation during solar flares is difficult due to the rarity of sufficiently isolated EUV-enhancements. Past work investigating the role of EUV-enhancements has been based on simulations only. This study focuses on the analysis of the response of the thermosphere to relatively long-lasting (between 1 and 2 days) EUV-enhancements. These events take place in isolation from coronal mass ejections, but often occur during the recovery phase of flare events. Using the Gravity Recovery and Climate Experiment and Challenging Minisatellite Payload accelerometer-derived density datasets, we show that the EUV-enhancements slow the thermosphere's recovery from a flare, and maintain a high level density perturbation “plateau” lasting several hours. The level of disturbance was found to be between 30% and 70% compared to the thermosphere's density without any disturbance. The duration of this plateau is long enough that it may be important for estimating satellite drag. Over the duration of the EUV-enhancements, Dst drops are also observed, indicating ring current activity. The proposed physical mechanism driving the Dst changes is linked to the increased production of O+ ions of ionospheric origin, which may occur over the EUV-enhancement period.