If you are carrying out a mid-level analysis (e.g., cross-sessions) that will be fed into an even higher-level analysis (e.g., cross-subjects), then it could be argued that a mixed-effects analysis should be done at the mid-level. A mixed-effects analysis would assume that the sessions are randomly sampled from a "population" of sessions that that subject could produce. This includes estimation of each subject's session-to-session variance. However, it is common for only a small number of sessions to be collected for each subject, making estimation of each subject's session-to-session variance impractical. One solution to this is to assume a common session-to-session variance for all subjects, thereby providing enough data for the session-to-session variance to be estimated. However, this has a downside in that you lose information about which subjects are good (i.e. low variance) and which subjects are bad (i.e. high variance). Hence, when only a small number of sessions has been collected for each subject (say, less than 10), it is recommended that you use a fixed effects analysis at the mid-level. This in effect treats the multiple first-level sessions (for each subject) as if they were one long session. Although this does ignore the session-session variability at this level, it is arguable that this is not of interest anyway (this is a somewhat philosophical debate). However, the combined session and subject variability will still affect (and be estimated at) the next level. 

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In short, fixed effects is favoured as it avoids practical problems associated with estimating the session-to-session variance (when there are not many sessions per subject), at the same time as maintaining information about which subjects are good and bad.