Abstract Long-lasting episodes of high accretion can strongly impact stellar and planetary formation. However, the universality of these events during the formation of young stellar objects (YSOs) is still under debate. Accurate statistics of strong outbursts (FUors) are necessary to understand the role of episodic accretion bursts. In this work, we search for a population of FUors that may have gone undetected in the past because they either (a) went into outburst before the start of modern monitoring surveys and are now slowly fading back into quiescence or (b) are slow-rising outbursts that would not commonly be classified as candidate FUors. We hypothesize that the light curves of these outbursts should be well fitted by linear models with negative (declining) or positive (rising) slopes. The analysis of the infrared light curves and photometry of ∼99,000 YSO candidates from SPICY yields 717 candidate FUors. Infrared spectroscopy of 20 candidates, from both the literature and obtained by our group, confirms that 18 YSOs are going through long-term outbursts and identifies two evolved sources as contaminants. The number of candidate FUors combined with previously measured values of the frequency of FUor outbursts yields average outburst decay times that are 2.5 times longer than the rise times. In addition, a population of outbursts with rise timescales between 2000 and 5000 days must exist to obtain our observed number of YSOs with positive slopes. Finally, we estimate a mean-burst lifetime of between 45 and 100 yr.