Hi Jeff,
Some interesting points I found instantly whilst checking out the link profile. I'll give my initial findings now and then examine them afterwards to summarize soon.
You have 569 links (out of a total of 2399 links that I checked to your site, this is a huge portion of your link profile) using the anchor text "twin prams". Every single one comes from the same domain (babyandco.com). You do not rank for this term in Google.
You have a fair few links using the anchor text "quinny prams". This time, they are from various domains and not one domain. You do not rank for this term in Google.
You have a fair few links using the anchor text "pushchair" again from various domains. You do not rank for this term.
The above also applies for Prams, Pram Systems, Baby Car Seats & Baby Buggies.
I would hazard a guess that your Google analytics shows drops in visitors coming on to your site from searching these terms. How do you feel about letting me have a look?
I think your link profile, while not terribly horrific, certainly isn't anywhere near natural or clean. I think that there could also be other issues playing a part. If I can access your analytics I can check out visitor drop dates and cross reference against Penguin and Panda algo updates to see if there could also be a content issue.
Here are a few links pointing to you site which are pretty toxic links (either deindexed from Google or have horrific trust signals):
EDIT: Removed the backlinks. I'm sure Moz don't want to be linking to these sites!
http://abdulmohideen.fastpage.name/litesun
http://bargainbabygear.info/otherresources/browse/73/quinnypushchair.html
http://pram-stroller.com/choosing-baby-car-seats-bytrevor-hobbs/
http://www.stufftobuyforbaby.co.uk/cheap-baby-stuff/cheap-prams-and-pushchairs-uk/
http://nursing-australia.com/baby-lo-nursing-chair/
I can give you a full list if you like. I would not submit these to Google Disavow unless you have received a warning though. Instead, you should use it to contact the owners of the sites to get them to remove the links. In total, Link Research Tools shows that you have 7% of incoming links being toxic.
A few questions/notes:
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Has the site got any sister sites, old owned sites, micro sites, niche sites etc 301 redirected to it that you know of? (other than the .com version I mention below)
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Did you receive an unnatural link message from Google?
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Can you give me a list of maybe 5 competitors so I can check out their backlink profile please.
Perhaps most worrying is that babys-mart.com redirects to the .co.uk version. The .com version has been deindexed by Google. This could be causing problems and is a big issue. It will pass on some very bad trust signals.