We investigate characteristics of electron acceleration during the late impulsive phase of large flares. Specifically, whether characteristic parameters of the acceleration process change during the late phase acceleration during the same event. We present X-ray (HXR) and microwave (MW) observations of the late impulsive phase from seven M- and X-class flares with insignificant heating. All these peaks are consistent with the absence of Neupert effect where the derivative of the thermal emission is flat, similarly to the flare reported by Warmuth et al. 2009. The X-ray spectral fits from RHESSI are consistent with a higher-than-usual low-energy cutoff value (> 70 keV). This is inferred from RHESSI spatially integrated spectra and spectroscopic imaging using an extended collisional thick target model (ECTTM), where electron propagation mechanisms such as the co-spatial return current, warm target and magnetic mirroring are also considered. Radio/MW emission from these peaks reveals an additional sub-group where 4/7 flares are associated with an increase and 3/7 with a decrease in magnetic field strengths compared to the main impulsive phase. The gradual (impulsive) peaks have a higher (lower) emission and are associated with increased (decreased) magnetic field strengths compared to earlier HXR peaks, except one flare which exhibits characteristics of gradual and impulsive events. Magnetograms further show that the HXR footpoints move into a region of increased magnetic field for gradual events. No such evidence is observed for the impulsive peaks. The main result is that these late peaks are consistent with a higher-than-usual injected low-energy cutoff and a total injected flux density insufficient to significantly heat the solar atmosphere compared to the initial HXR impulsive phase.