We searched through roughly 12 years of archival survey data acquired by the Katzman Automatic Imaging Telescope (KAIT) as part of the Lick Observatory Supernova Search (LOSS) in order to detect or place limits on possible progenitor outbursts of Type IIn supernovae (SNe~IIn). The KAIT database contains multiple pre-SN images for 5 SNe~IIn (plus one ambiguous case of a SN IIn/imposter) within 50 Mpc. No progenitor outbursts are found using the false discovery rate (FDR) statistical method in any of our targets. Instead, we derive limiting magnitudes (LMs) at the locations of the SNe. These limiting magnitudes (typically reaching $m_R approx 19.5,mathrm{mag}$) are compared to outbursts of SN 2009ip and $eta$ Car, plus additional simulated outbursts. We find that the data for SN 1999el and SN 2003dv are of sufficient quality to rule out events $sim40$ days before the main peak caused by initially faint SNe from blue supergiant (BSG) precursor stars, as in the cases of SN 2009ip and SN 2010mc. These SNe~IIn may thus have arisen from red supergiant progenitors, or they may have had a more rapid onset of circumstellar matter interaction. We also estimate the probability of detecting at least one outburst in our dataset to be $gtrsim60%$ for each type of the example outbursts, so the lack of any detections suggests that such outbursts are either typically less luminous (intrinsically or owing to dust) than $sim -13,mathrm{mag}$, or not very common among SNe~IIn within a few years prior to explosion.
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